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Georgian Mathematical Journal

Editors-in-Chief: Ivane Kiguradze und Tengiz Buchukuri
Wissenschaftlicher Beirat: Maia Kvinikadze , O.V. Besov , B. Bojarski , Pavel Drábek , R. Duduchava , Hans-Jürgen Engelbert , Lasha Ephremidze , R. Gamkrelidze , Hvedri Inassaridze , M. Jibladze , T. Kadeishvili , Otto H. Kegel , Alexander Kharazishvili , S. Kharibegashvili , E. Khmaladze , Tariel Kiguradze , S. I. Krushkal , J. Kurzweil , S. Kwapien , Hans Rudolf Lerche , Michael Mania , Jean Mawhin , A. Meskhi , P.E. Ricci , V. Tarieladze , Hans Triebel und Fabio Zanolin

Sprache: Englisch

Erstveröffentlichung: 1. Februar 1994

Erscheinungsweise: 6 Hefte pro Jahr

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Über diese Zeitschrift

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The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.

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Banach algebra structure in analytic tent spaces

29. August 2025

Rong Yang, Xiangling Zhu

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In this paper, the Duhamel product is used to endow analytic tent spaces with a Banach algebra structure. The Hadamard–Bergman convolution on these spaces is also described. Additionally, the Deddens algebras of composition operators are studied.
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A series representation for the Catalan constant

29. August 2025

Horst Alzer

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We prove the following series representation for the Catalan constant G : G = 3 10 - 48 ⁢ ∑ n = 0 ∞ 4 ⁢ n 2 + 8 ⁢ n - 9 ( 4 ⁢ n 2 - 4 ⁢ n + 5 ) ⁢ ( 4 ⁢ n 2 + 20 ⁢ n + 29 ) ⁢ S n 3 , G=\frac{3}{10}-48\sum_{n=0}^{\infty}\frac{4n^{2}+8n-9}{(4n^{2}-4n+5)(4n^{2}+20% n+29)}S_{n}^{3}, where S n = ∑ k = 0 n ( - 1 ) k 2 ⁢ k + 1 S_{n}=\sum_{k=0}^{n}\frac{(-1)^{k}}{2k+1} is the n th partial sum of the classical Leibniz series for π 4 {\frac{\pi}{4}} .
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Modeling and numerical analysis of a viscoelastic contact problem for locking materials with time-fractional derivatives

29. August 2025

Jinxia Cen, Mustapha Bouallala, Abdesadik Bendarag

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This article explores a new contact problem involving viscoelastic materials locked with a rigid foundation. The constitutive relation in our study is constructed using a fractional Kelvin–Voigt model to describe displacement behavior. The contact is characterized by a variation of the Signorini condition, while friction is modeled by a nonlocal Coulomb’s friction law. We present the mathematical model for the viscoelastic process, provide the variational formulation, and establish the existence of a solution. We present fully discrete finite element schemes for the variational problem and derive error estimates for the approximations.
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An introduction to fractal Lebesgue integral

29. August 2025

Hemanta Kalita, Alireza K. Golmankhanehand

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This manuscript explores various characteristics of generalized fractal measures. We expand the concept of fractal integrals in relation to step functions and examine their numerous properties. Notably, since all step functions are classified as simple functions, we apply the aforementioned generalized measure to introduce Lebesgue-type integrals, referred to as FL -integrals. Additionally, we demonstrate that all F α {F^{\alpha}} -integrable functions are FL -integrals. Lastly, we address the bounded convergence theorem within the context of fractals.
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On power series strong and statistical convergences for double sequences via Orlicz functions

29. August 2025

Nilay Şahin Bayram, Sevda Yıldız

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The present paper introduces the notions of strong P p 2 {P_{p}^{2}} -convergence and P p 2 {P_{p}^{2}} -statistical convergence for double sequences with respect to an Orlicz function. Based on these new notions of convergence, new double sequence spaces and some of their properties are given. Furthermore, certain inclusion relations are analyzed. Finally, we observe that, under proper choices, the analogous results can be obtained for modulus function.
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Singular value and norm bounds for accretive-dissipative matrices

29. August 2025

Wasim Audeh, Hamid Reza Moradi, Mohammad Sababheh

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This paper discusses possible new bounds for the singular values and unitarily invariant norms of accretive-dissipative matrices. The obtained bounds are possible generalizations for certain known results from the context of positive matrices to the context of accretive-dissipative ones.
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Semigroup real characters generated by quasicharacters

29. August 2025

Gastão Bettencourt, Sérgio Mendes

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Let S be an infinite, finitely generated semigroup, endowed with a probability measure. Based on the work [A. Erschler and A. Karlsson, Homomorphisms to ℝ \mathbb{R} constructed from random walks, Ann. Inst. Fourier (Grenoble) 60 2010, 6, 2095–2113], we construct a real character of S using a random walk approach. In our construction, the word length used in Erschler and Karlsson’s work is replaced by a quasicharacter.
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Dolbeault’s theorem for sheaves of pseudoanalytic differential forms

1. August 2025

Irakli Sikharulidze

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A way is presented to extend the notion of pseudoanalyticity of the Bers–Vekua theory to differential forms defined on a complex manifold. A sheaf is defined whose sections over an open subset are differential forms whose component functions with respect to any trivializing sections satisfy in each argument the linear Carleman–Bers–Vekua equation. Such a sheaf can be defined as the kernel sheaf of an appropriate sheaf homomorphism. For it, under certain conditions, an analogue of the Poincaré lemma is valid and, under the same conditions, the sequence of such sheaf homomorphisms forms a complex, which makes is possible to prove an analogue of the Dolbeault’s theorem for these sheaves.
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On generalized bounded variation functions on Vilenkin groups and applications

1. August 2025

Ushangi Goginava, Gvantsa Shavardenidze, Tadael Mequanent, Yonathan Demeke

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In the present paper, we introduce certain classes of functions of weighted bounded oscillation on bounded Vilenkin groups. For such classes, we employ the summability methods of the theory of double Vilenkin–Fourier series.
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Commutativity of Banach algebras involving endomorphisms

25. Juli 2025

Mohammadi El Hamdaoui

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In this article, we present new contributions to the study of endomorphisms within algebraic structures, particularly focusing on prime Banach algebras. We establish that any prime Banach algebra must be commutative if it admits endomorphisms and multipliers satisfying specific algebraic identities. Our main results generalize several known theorems. Additionally, we provide an illustrative example demonstrating that the primeness assumption in several theorems is indeed essential.
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Proof of time evolution integration theorems in calculus for moving surfaces

18. Juli 2025

David V. Svintradze

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We present a rigorous proof of the time evolution integration theorems that suitably extend differential geometry to the calculus of moving surfaces. This proof demonstrates that the calculus of moving surfaces is a complete extension of differential geometry to the dynamic manifolds.
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The properties of Banach algebras affected by differential identities

18. Juli 2025

Mohamed Moumen, Lahcen Taoufiq

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Let ℬ {\mathcal{B}} be a Banach algebra. The interest of this article lies in the study of the commutativity of ℬ {\mathcal{B}} if certain specific algebraic identities hold over a non-empty open subset of ℬ {\mathcal{B}} . The limitations imposed in the hypothesis of our results are justified by some examples.
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On properties of weakly locally compact commutative groups

18. Juli 2025

Onise Surmanidze

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The paper presents an algebraic characterization of a twist-free weakly locally compact group whose factor group is linearly compact with respect to the zero component. It is shown that the local direct product of weakly locally compact groups is weakly locally compact. Additionally, a necessary and sufficient condition is established for determining when a weakly locally compact group G , containing a given subgroup H , can be decomposed into a local direct product of subgroups of rank one.
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Generalized Volterra integral operators on weighted Fock spaces induced by A ∞ -type weights

18. Juli 2025

Chunxu Xu

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In this paper, we study the generalized Volterra integral operators T g n , m ⁢ f ⁢ ( z ) = ∫ 0 z f ( n ) ⁢ ( w ) ⁢ g ( m ) ⁢ ( w ) ⁢ 𝑑 w T_{g}^{n,m}f(z)=\int_{0}^{z}f^{(n)}(w)g^{(m)}(w)\,dw acting on the weighted Fock spaces F α , ω p {F_{\alpha,\omega}^{p}} , where ω is a weight satisfying certain restricted A ∞ {A_{\infty}} -conditions. Using a unified approach, the boundedness, compactness, and essential norm of the generalized Volterra integral operators T g n , m : F α , ω 1 p → F β , ω 2 q {T_{g}^{n,m}:F_{\alpha,\omega_{1}}^{p}\rightarrow F_{\beta,\omega_{2}}^{q}} for all 0 < p , q < ∞ {0<p,q<\infty} are completely characterized. As an application, we generalize our results to the Fock–Sobolev-type spaces.
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Multiplicative Lie algebra structure on a nilpotent group of class 2

9. Juli 2025

Deepak Pal, Amit Kumar, Sumit Kumar Upadhyay

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This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class 2.
Open Access
Dilation estimates for Orlicz amalgam spaces on the affine group

9. Juli 2025

Büşra Arıs

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Let 𝔸 {\mathbb{A}} be the affine group and let Φ 1 , Φ 2 {\Phi_{1},\Phi_{2}} be Young functions. We study the Orlicz amalgam spaces W ⁢ ( L Φ 1 ⁢ ( 𝔸 ) , L Φ 2 ⁢ ( 𝔸 ) ) {W(L^{\Phi_{1}}(\mathbb{A}),L^{\Phi_{2}}(\mathbb{A}))} defined on 𝔸 {\mathbb{A}} , where the local and global component spaces are the Orlicz spaces L Φ 1 ⁢ ( 𝔸 ) {L^{\Phi_{1}}(\mathbb{A})} and L Φ 2 ⁢ ( 𝔸 ) {L^{\Phi_{2}}(\mathbb{A})} , respectively. In this paper, we obtain norm estimates of the dilation operator on the amalgam space W ⁢ ( L Φ 1 ⁢ ( 𝔸 ) , L Φ 2 ⁢ ( 𝔸 ) ) {W(L^{\Phi_{1}}(\mathbb{A}),L^{\Phi_{2}}(\mathbb{A}))} using constructions related to the affine group 𝔸 {\mathbb{A}} .
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Boundary value problem with Dirichlet, Neumann and Robin conditions on separate parts of the boundary for an inhomogeneous equation of string vibration

9. Juli 2025

Otar Jokhadze, Sergo Kharibegashvili

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In this paper, the well-posedness of a boundary value problem for an inhomogeneous equation of string vibration with Dirichlet, Neumann and Robin conditions on separate parts of the boundary is proved. In this case, the solution is given in quadratures. If the Robin condition turns into the Neumann condition, then the problem becomes ill-posed. In particular, it is shown that the corresponding homogeneous problem has an infinite number of linearly independent solutions that can be written explicitly.
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On a fourth-order Leray–Lions problem involving s(x)-Hardy potential and singular nonlocal source term

9. Juli 2025

Mohamed Karim Hamdani, Khaled Kefi, Romulo Diaz Carlos, Zeineb Klai

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This paper investigates the existence of at least two distinct weak solutions using Bonanno’s theorem [G. Bonanno, Relations between the mountain pass theorem and local minima, Adv. Nonlinear Anal. 1 (2012), no. 3, 205–220, Theorem 3.2], and establishes the existence of no fewer than two nontrivial weak solutions through the Bonanno–D’Aguì theorem [G. Bonanno and G. D’Aguì, Two nonzero solutions for elliptic Dirichlet problems, Z. Anal. Anwend. 35 (2016), no. 4, 449–464, Theorem 2.1] applied to a general class of fourth-order Leray–Lions problems that include an s ⁢ ( x ) {s(x)} -Hardy potential and a nonlocal singular term.
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Finite groups in which every maximal invariant subgroup of order divisible by p is nilpotent

9. Juli 2025

Jiangtao Shi, Mengjiao Shan, Fanjie Xu

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Let A and G be finite groups such that A acts coprimely on G by automorphisms. For any fixed prime divisor p of | G | {|G|} , we provide a complete characterization of the structure of a group G in which every maximal A -invariant subgroup of order divisible by p is nilpotent.
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A q-analog of Schröder sequence spaces and compact operators

9. Juli 2025

Muhammet Çihat Dağli, Taja Yaying, Mohammed Mursaleen

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We introduce q -analog of Schröder matrix and discuss its domains in the spaces c and c 0 {c_{0}} . Also, the Schauder basis and α-, β-, γ-duals are given and certain classes of matrix mappings are characterized on these spaces. Moreover, the characterizations of certain compact operators are established via Hausdorff measure of noncompactness.
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Martingale Hardy spaces and some new weighted maximal operators of partial sums of Walsh–Fourier series

28. Juni 2025

Davit Baramidze

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In this paper, we introduce some new weighted maximal operators of the partial sums of the Walsh–Fourier series. We prove that for some “optimal” weights these operators indeed are bounded from the martingale Hardy space H p ⁢ ( G ) {H_{p}(G)} to the Lebesgue space L p ⁢ ( G ) {L_{p}(G)} for 0 < p < 1 {0<p<1} . Moreover, we also prove the sharpness of this result. As a consequence, we obtain some new and well-known results.
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Weighted estimates for commutators of multilinear singular integral operators in Dunkl setting

28. Juni 2025

Yan Wang, Fanghui Liao, Zongguang Liu

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In this paper, we study multilinear Dunkl–Calderón–Zygmund operators, focusing on both the establishment of endpoint estimates for the operators and the boundedness of two types of commutators generated by these operators and BMO d {\mathrm{BMO}_{d}} functions, as demonstrated through sharp maximal function estimates.
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Power inequalities for weighted numerical radius and norm of operators

25. Juni 2025

Najla Altwaijry, Silvestru Sever Dragomir, Kais Feki

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For a bounded linear operator T on a complex Hilbert space ℋ {\mathcal{H}} , we define the weighted real and imaginary parts of the operator T as ℜ t ⁢ ( T ) := ( 1 - t ) ⁢ T ∗ + t ⁢ T {\mathfrak{R}_{t}(T):=(1-t)T^{\ast}+tT} and ℑ t ⁢ ( T ) := ( 1 - t ) ⁢ T - t ⁢ T ∗ i {\mathfrak{I}_{t}(T):=\frac{(1-t)T-tT^{\ast}}{i}} for t ∈ [ 0 , 1 ] {t\in[0,1]} , where T ∗ {T^{\ast}} denotes the adjoint operator of T . By setting T t := ℜ t ⁢ ( T ) + i ⁢ ℑ t ⁢ ( T ) {T_{t}:=\mathfrak{R}_{t}(T)+i\mathfrak{I}_{t}(T)} , we define the weighted norm ∥ T ∥ t := ∥ T t ∥ {\|T\|_{t}:=\|T_{t}\|} . Another weighted numerical radius is given by w ~ t ⁢ ( T ) = sup ⁡ { ∥ ℜ t ⁢ ( e i ⁢ φ ⁢ T ) ∥ : φ ∈ ℝ } {\widetilde{w}_{t}(T)=\sup\{\|\mathfrak{R}_{t}(e^{i\varphi}T)\|:\varphi\in% \mathbb{R}\}} for t ∈ [ 0 , 1 ] {t\in[0,1]} . In this paper, we present new power inequalities for the weighted operator norm ∥ ⋅ ∥ t {\|\cdot\|_{t}} and the weighted numerical radius w ~ t ⁢ ( ⋅ ) {\widetilde{w}_{t}(\,\cdot\,)} . Additionally, we discuss the special cases of the classical numerical radius and norm of Hilbert space operators.
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Existence of positive weak solutions for fractional Laplacian elliptic systems

19. Juni 2025

José Vanterler da Costa Sousa, Leandro S. Tavares, Nguyen Thanh Chung

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In this paper, we focus on studying the existence of positive weak solutions for a class of fractional Laplacian systems with respect to another function ψ ⁢ ( ⋅ ) {\psi(\,\cdot\,)} with multiple parameters. These systems arise in various applications, such as Lévy flights. We establish new conditions for the existence of a positive solution for the considered system using the method of sub-super solutions, which extends and complements previously known results in the literature.
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Trudinger-type inequalities in Musielak–Orlicz spaces over metric measure spaces

18. Juni 2025

Takao Ohno, Tetsu Shimomura

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Our aim in this note is to deal with Trudinger-type inequalities for variable Riesz potentials of functions in Musielak–Orlicz spaces over bounded metric measure spaces as an extension of the previous paper by Hurri-Syrjänen and the authors ( Complex Var. Elliptic Equ. 68 (2023), no. 10, 1694–1714). As an application, we prove Trudinger-type inequalities for double phase functionals.
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Weak-type estimates for variable Riesz potentials with respect to the Hausdorff content over metric measure spaces

17. Juni 2025

Toshihide Futamura, Yoshihiro Sawano, Tetsu Shimomura

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We are concerned with weak-type estimates for variable Riesz potentials I α ⁢ ( ⋅ ) , τ ⁢ f {I_{\alpha(\,\cdot\,),\tau}f} with respect to variable dimensional Hausdorff content over bounded metric measure spaces X equipped with lower Ahlfors Q ⁢ ( ⋅ ) {Q(\,\cdot\,)} -regular measures. As an application, we give an exponential integrability for I α ⁢ ( ⋅ ) , τ ⁢ f {I_{\alpha(\,\cdot\,),\tau}f} with respect to variable dimensional Hausdorff content.
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Iteration method for the Dirichlet problem of the elasticity theory

17. Juni 2025

David Natroshvili

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We construct a convergent recurrence scheme for a solution of the three-dimensional Dirichlet boundary value problem of the elasticity theory. By the potential method, the Dirichlet problem is reduced to the uniquely solvable Fredholm integral equation of the first kind with a weakly singular boundary integral operator generated by the single layer potential. First, we construct a sequence of successive approximations which converges to the solution of the boundary integral equation in appropriate Bessel-potential spaces of functions defined on the boundary. Afterwards, using these approximations as densities of the single layer potential, we formulate another iteration which converges to the solution of the Dirichlet boundary value problem in the appropriate Sobolev–Slobodetskii spaces of functions defined in the region occupied by the elastic body.
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C-Gorenstein projective, injective, flat modules and trivial ring extensions

17. Juni 2025

Lixin Mao

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Let C be a semidualizing module over a commutative ring R and let R ⋉ C {R\ltimes C} be the trivial extension of R by C . We prove that (1) ( M , f ) {(M,f)} is a Gorenstein projective R ⋉ C {R\ltimes C} -module if and only if M is a C -Gorenstein projective R -module; (2) [ M , g ] {[M,g]} is a Gorenstein injective R ⋉ C {R\ltimes C} -module if and only if M is a C -Gorenstein injective R -module; (3) if R is a coherent ring, then ( M , f ) {(M,f)} is a Gorenstein flat R ⋉ C {R\ltimes C} -module if and only if M is a C -Gorenstein flat R -module. Some applications of these results are given.
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Highly accurate compact difference schemes for multidimensional delay Schrödinger equations

17. Juni 2025

Allaberen Ashyralyev, Deniz Agirseven, Baris Erköse

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In present paper, the second-order accurate stable compact difference schemes (DSs) for the delay Schrödinger-type partial differential equation (DSPDE) in a Hilbert space are constructed. The stability of these DSs is established. As applications, stability estimates (SEs) for the solutions of DSs for two types of DSPDEs are derived. A numerical method is proposed for solving one and two-dimensional DSPDEs.
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On certain new characterizations of weights in higher order Wirtinger-type inequalities via time scales calculus

17. Juni 2025

Mahmoud M. Osman, Mario Krnić, Ravi P. Agarwal, Samir H. Saker

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In this paper, we establish a new characterization of weights in dynamic inequality of Wirtinger’s type involving higher order delta derivatives on time scales. More precisely, conditions on nonnegative rd-continuous weighted functions u and υ are given which ensure that a mixed norm dynamic inequality of the form ∥ ψ σ ∥ 𝕃 u q q ⁢ ( [ a , ∞ ) 𝕋 ) ≤ C ⁢ ∥ ψ Δ n ∥ 𝕃 υ p p ⁢ ( [ a , ∞ ) 𝕋 ) , \|\psi^{\sigma}\|_{\mathbb{L}_{u^{q}}^{q}([a,\infty)_{\mathbb{T}})}\leq C\big{% \|}\psi^{\Delta^{n}}\big{\|}_{\mathbb{L}_{\upsilon^{p}}^{p}([a,\infty)_{% \mathbb{T}})}, holds for 1 < p ≤ q ≤ p ′ {1<p\leq q\leq p^{\prime}} , p ′ = p p - 1 {p^{\prime}=\frac{p}{p-1}} and ψ ∈ C r ⁢ d ( n ) ⁢ ( [ a , ∞ ) 𝕋 , ℝ ) {\psi\in C_{rd}^{(n)}([a,\infty)_{\mathbb{T}},\mathbb{R})} . As a special case, these results encompass the results obtained for integral inequalities when 𝕋 = ℝ {\mathbb{T=R}} , for the discrete inequalities when 𝕋 = ℕ {\mathbb{T=N}} , and for the quantum inequalities of quantum series when 𝕋 = q ℕ {\mathbb{T=}q^{\mathbb{N}}} .
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Oscillatory singular integrals with radial rough kernel and fewnomials phases

17. Juni 2025

Boyu Jiang

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In this paper, we study oscillatory singular integrals with radial rough kernels: T Q , h ⁢ f ⁢ ( x ) = p.v. ⁢ ∫ ℝ n f ⁢ ( x - y ) ⁢ Ω ⁢ ( y ) ⁢ h ⁢ ( | y | ) | y | n ⁢ e i ⁢ Q ⁢ ( | y | ) ⁢ d y , T_{Q,h}f(x)=\text{ p.v. }\int_{\mathbb{R}^{n}}f(x-y)\frac{\Omega(y)h(|y|)}{|y|% ^{n}}e^{iQ(|y|)}\,\mathrm{d}y, where Q ⁢ ( t ) {Q(t)} is a real polynomial on ℝ {\mathbb{R}} , Ω ∈ H ⁢ ( S n - 1 ) {\Omega\in H(S^{n-1})} is a homogeneous function of degree zero on the unit sphere S n - 1 {S^{n-1}} with vanishing mean value, and h satisfies the following conditions: 1 R ⁢ ∫ 0 R | h ⁢ ( t ) | q ⁢ d t ≤ C , | 1 p - 1 2 | < min ⁡ { 1 2 , 1 q ′ } , \frac{1}{R}\int_{0}^{R}|h(t)|^{q}\,\mathrm{d}t\leq C,\quad\bigg{|}\frac{1}{p}-% \frac{1}{2}\bigg{|}<\min\biggl{\{}\frac{1}{2},\frac{1}{q^{\prime}}\bigg{\}}, where C is a constant independent of R > 0 {R>0} , and h is the radial rough kernel. Under the assumption Ω ∈ H 1 ⁢ ( S n - 1 ) {\Omega\in H^{1}(S^{n-1})} , we prove that T Q , h {T_{Q,h}} is bounded on the Lebesgue space L p {L^{p}} for 1 < p < ∞ {1<p<\infty} , provided that h satisfies aforementioned condition. The methods we mainly use are created by S. Guo.
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The variational properties of general Fourier coefficients of functions with derivatives of finite variation

29. Mai 2025

Vakhtang Tsagareishvili, Ani Kashibadze

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In the present paper, we consider problems of convergence of a special series of moduli of the difference of the general Fourier coefficients of functions with derivatives of finite variation with respect to general orthonormal systems (ONS). It is shown that such series with respect to the Haar system or ( 2 ⁢ cos ⁡ 2 ⁢ π ⁢ n ⁢ x ) {(\sqrt{2}\cos 2\pi nx)} system are convergent for functions with derivatives of finite variation. Furthermore, it is proved that, with respect to general ONS, this series, in general, does not converge. Also, we find the optimal condition that needs to be imposed on the functions of the ONS so that the general orthonormal systems, possessing the properties similar to the Haar system, converge for functions with derivatives of finite variation.
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A property of Cauchy–Stieltjes kernel families based on dilation of measures

29. Mai 2025

Ibrahim-Elkhalil Ahmed, Ayed R. A. Alanzi, Raouf Fakhfakh

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In this paper, we introduce a property of the inverse Semicircle and the free Gamma laws based on the dilation of measures in the context of Cauchy–Stieltjes Kernel (CSK) families. Assume that the CSK family produced by a non-degenerate probability measure λ on ℝ {\mathbb{R}} with support limited from above is ℱ + ⁢ ( λ ) = { 𝒬 m λ ⁢ ( d ⁢ y ) : m ∈ ( m 1 λ , m + λ ) } {\mathcal{F}_{+}}(\lambda)=\{\mathcal{Q}_{m}^{\lambda}(dy):m\in(m_{1}^{\lambda% },m_{+}^{\lambda})\} . For α ∈ ℝ ∖ 0 {\alpha\in\mathbb{R}\setminus 0} , consider 𝐇 α {\mathbf{H}_{\alpha}} , x ↦ α ⁢ x {x\mapsto\alpha x} and provide the set of measures 𝐇 α ⁢ ( ℱ + ⁢ ( λ ) ) = { 𝐇 α ⁢ ( 𝒬 m λ ⁢ ( d ⁢ y ) ) : m ∈ ( m 1 λ , m + λ ) } . \mathbf{H}_{\alpha}({\mathcal{F}_{+}}(\lambda))=\{\mathbf{H}_{\alpha}(\mathcal% {Q}_{m}^{\lambda}(dy)):m\in(m_{1}^{\lambda},m_{+}^{\lambda})\}. Let us say that α > 0 {\alpha>0} . We demonstrate that if 𝐇 α ⁢ ( ℱ + ⁢ ( λ ) ) {\mathbf{H}_{\alpha}({\mathcal{F}_{+}}(\lambda))} is a re-parametrization of ℱ + ⁢ ( λ ) {{\mathcal{F}_{+}}(\lambda)} (i.e., 𝐇 α ⁢ ( ℱ + ⁢ ( λ ) ) = ℱ + ⁢ ( λ ) {\mathbf{H}_{\alpha}({\mathcal{F}_{+}}(\lambda))={\mathcal{F}_{+}}(\lambda)} ), then λ is either the free Gamma type law or the inverse Semicircle type law up to scaling.
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Approximation of Kantorovich-type max-product q-Bernstein operators

29. Mai 2025

Sezin Cit, Carmen Violeta Muraru, Ogün Dogru

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In this article, we show that the approximation order of Kantorovich-type max-product Bernstein operators can be improved. We are able to obtain a better approximation order for q -Bernstein operators. In addition, we present a Kantorovich-type generalization of max-product operators based on q -integers. In particular, we find the approximation order (via the classical modulus of continuity) of the Kantorovich-type max-product q -Bernstein operator.
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Equation characterizations of normal matrices

29. Mai 2025

Yu Tao, Xiang Ji, Junchao Wei

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In this paper, we discuss many new characterizations of normal matrices by using the representations of the solutions to constructed equations.
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A Cauchy–Kowalevski theorem for ψ-bimonogenic functions

29. Mai 2025

José Luis Serrano Ricardo, Ricardo Abreu Blaya

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In this paper we prove a Cauchy–Kowalevski theorem for the solutions of the system ∂ x ψ ∂ x ψ f = 0 {{}^{\psi}\partial_{x}{}^{\psi}\partial_{x}f=0} , where ∂ x ψ {{}^{\psi}\partial_{x}} stands for the Cauchy–Riemann operator, associated to the orthonormal basis ψ of ℝ m + 1 {{\mathbb{R}}^{m+1}} .
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Characterizations of the boundedness of commutators of G-fractional integral operators in generalized G-Morrey spaces on ℝ₊

29. Mai 2025

Elman J. Ibrahimov, Alexander Meskhi

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Criteria for a pair of measurable functions ( ω 1 , ω 2 ) {(\omega_{1},\omega_{2})} ensuring the boundedness of the k -th order commutators J G b , α , k {J_{G}^{b,\alpha,k}} ( k = 1 , 2 , … {k=1,2,\dots} ) of the G -fractional integral from one generalized G -Morrey space ℳ p , γ , ω 1 ⁢ ( ℝ + ) {\mathcal{M}_{p,\gamma,\omega_{1}}(\mathbb{R}_{+})} to another one ℳ q , γ , ω 2 ⁢ ( ℝ + ) {\mathcal{M}_{q,\gamma,\omega_{2}}(\mathbb{R}_{+})} (resp. from ℳ 1 , γ , ω 1 ⁢ ( ℝ + ) {\mathcal{M}_{1,\gamma,\omega_{1}}(\mathbb{R}_{+})} to the weak space W ⁢ ℳ q , γ , ω 2 ⁢ ( ℝ + ) {W\mathcal{M}_{q,\gamma,\omega_{2}}(\mathbb{R}_{+})} ) are established. In the case when b ∈ BMO G ⁢ ( ℝ + ) {b\in\mathrm{BMO}_{G}(\mathbb{R}_{+})} and 1 < p < q < ∞ {1<p<q<\infty} , necessary and sufficient conditions on the pair ( ω 1 , ω 2 ) {(\omega_{1},\omega_{2})} are found, ensuring the boundedness of the operators J G b , α , k {J_{G}^{b,\alpha,k}} from ℳ p , γ , ω 1 ⁢ ( ℝ + ) {\mathcal{M}_{p,\gamma,\omega_{1}}(\mathbb{R}_{+})} to ℳ q , γ , ω 2 ⁢ ( ℝ + ) {\mathcal{M}_{q,\gamma,\omega_{2}}(\mathbb{R}_{+})} with 1 p - 1 q = α γ {\frac{1}{p}-\frac{1}{q}=\frac{\alpha}{\gamma}} . Necessary and sufficient conditions on the function ω are also found to guarantee the boundedness of the operator J G b , α {J_{G}^{b,\alpha}} from ℳ p , γ , ω ⁢ ( ℝ + ) {\mathcal{M}_{p,\gamma,\omega}(\mathbb{R}_{+})} to ℳ q , γ , ω p q ⁢ ( ℝ + ) {\mathcal{M}_{q,\gamma,\omega^{\frac{p}{q}}}(\mathbb{R}_{+})} provided that 1 < p < q < ∞ {1<p<q<\infty} .
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Boundedness of Marcinkiewicz integral operators on grand variable Herz–Hardy spaces

29. Mai 2025

Faiza Shabbir, Muhammad Asad Zaighum

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The aim of this paper is to prove the boundedness of Marcinkiewicz integral operators on grand variable Herz–Hardy spaces using the atomic decomposition of grand variable Herz–Hardy spaces already established.
Open Access
A generalized conditional Wiener integral with a drift and its applications

29. Mai 2025

Dong Hyun Cho

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Let C ⁢ [ 0 , T ] {C[0,T]} denote the space of real-valued continuous functions on [ 0 , T ] {[0,T]} and let Z e → , ∞ ⁢ ( x ) = ( x ⁢ ( 0 ) , ∫ 0 T e 1 ⁢ ( t ) ⁢ 𝑑 x ⁢ ( t ) , ∫ 0 T e 2 ⁢ ( t ) ⁢ 𝑑 x ⁢ ( t ) , … ) for x ∈ C ⁢ [ 0 , T ] , Z_{\vec{e},\infty}(x)=\Bigg{(}x(0),\int_{0}^{T}e_{1}(t)\,dx(t),\int_{0}^{T}e_{% 2}(t)\,dx(t),\dots\Bigg{)}\quad\text{for ${x\in C[0,T]}$,} where { e j } j = 1 ∞ {\{e_{j}\}_{j=1}^{\infty}} is a sequence of appropriate functions on [ 0 , T ] {[0,T]} . In this paper, we derive a simple evaluation formula for calculating Radon–Nikodym derivatives similar to the conditional Wiener integrals of functions on C ⁢ [ 0 , T ] {C[0,T]} given Z e → , ∞ {Z_{\vec{e},\infty}} which has an initial weight and a kind of drift. As applications of the formula, we evaluate the derivatives of various functions containing the time integral which is of interest in quantum mechanics, especially in Feynman integration theory.
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On Sylvester’s denumerants

30. April 2025

Eteri Samsonadze

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The paper deals with the problem of calculating Sylvester’s denumerant D ⁢ ( b ; a 1 , a 2 , … , a n ) {D(b;a_{1},a_{2},\dots,a_{n})} , i.e., the number D ⁢ ( b ) {D(b)} of integer non-negative solutions of an equation ∑ i = 1 n a i ⁢ x i = b {\sum_{i=1}^{n}a_{i}x_{i}=b} , where n ≥ 2 {n\geq 2} , a 1 , a 2 , … , a n {a_{1},a_{2},\dots,a_{n}} are natural numbers and b is a non-negative integer. Unlike traditional methods of finding denumerants, in our study we employ only elementary methods, mainly the properties of the Kronecker function and the elements of combinatorics. The formula is derived to express D ⁢ ( b ) {D(b)} , for an integer non-negative b , coprime a 1 , a 2 , … , a n {a_{1},a_{2},\dots,a_{n}} and s ≠ 0 {s\neq 0} , via D ⁢ ( r ) , D ⁢ ( r + M ) , … , D ⁢ ( r + ( s - 1 ) ⁢ M ) D(r),D(r+M),\dots,D(r+(s-1)M) , where s = [ n - ∑ i = 1 n a i + r M ] {s=[n-\frac{\sum_{i=1}^{n}a_{i}+r}{M}]} , M is the least common multiple of the numbers a 1 , a 2 , … , a n {a_{1},a_{2},\dots,a_{n}} , and r is the remainder of b modulo M . Note that s takes quite small values in some particular cases. Moreover, the recurrent formulas are derived to calculate D ⁢ ( b ) {D(b)} for any non-negative integer b . These formulas, in particular, are used in finding D ⁢ ( r ) , D ⁢ ( r + M ) , … , D ⁢ ( r + ( s - 1 ) ⁢ M ) {D(r),D(r+M),\dots,D(r+(s-1)M)} . For the case where s = 0 {s=0} and a 1 , a 2 , … , a n {a_{1},a_{2},\dots,a_{n}} are coprime, the explicit formula D ⁢ ( b , a 1 , a 2 , … , a n ) = M n - 1 a 1 ⁢ a 2 ⁢ ⋯ ⁢ a n ⁢ ( b ′ + n - 1 n - 1 ) {D(b,a_{1},a_{2},\dots,a_{n})=\frac{M^{n-1}}{a_{1}a_{2}\cdots a_{n}}{\bigl{(}% \begin{smallmatrix}b^{\prime}+n-1\\ n-1\\ \end{smallmatrix}\bigr{)}}} is given (here b ′ = [ b M ] {b^{\prime}=[\frac{b}{M}]} ). To illustrate the proposed method, examples of finding the function D ⁢ ( b ) {D(b)} for linear Diophantine equations with 2 , 3 , 4 , 7 , 10 {2,3,4,7,10} and n variables are given.
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A note on the localizations of generalized injective modules

26. April 2025

Xiaolei Zhang

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Let R be a ring and let S be a multiplicative subset of R . In this note, we study the localization of S -injective modules and u - S -injective modules under S -Noetherian rings and u - S -Noetherian rings, respectively. The u - S -absolutely pure property is showed to be preserved under localizations over u - S -coherent rings. Besides, we give an example to show the difference between S -injective modules and u - S -injective modules, and some counter-examples to deny questions proposed in [J. Baeck, S -injective modules, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 118 2024, 1, Paper No. 20].
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Number of zeros of solutions of second order linear ordinary differential equation

26. April 2025

Monika Dosoudilová, Alexander Lomtatidze

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An integral condition for the existence of at least n zeros for any solution of a second order linear equation is established.
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Precompact sets in matrix weighted Lebesgue spaces with variable exponent

26. April 2025

Shengrong Wang, Pengfei Guo, Jingshi Xu

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In this paper, we first give a sufficient condition for precompactness in the matrix-weighted Lebesgue spaces with variable exponent by translation. Then we obtain a criterion for precompactness in the matrix-weighted Lebesgue spaces with variable exponent by average. Next, we give a criterion for precompactness in the matrix-weighted Lebesgue spaces with variable exponent by approximate identity. Finally, precompactness in the matrix-weighted Sobolev spaces with variable exponent is also considered.
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Gamma-type operators and composition

26. April 2025

Vijay Gupta, Vaibhav Sharma

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In the present article, we examine the approximation properties of certain Gamma-type operators. Precisely, we consider the compositions of Rathore and Lupaş operators. We estimate the moments of the new composition operators and provide their probabilistic interpretation as well. Then, we provide some convergence results and their difference estimates, while focusing on the preservation of the moduli of smoothness of first- and second-order, using a stochastic approach. Additionally, Korovkin-type theorems and Voronovskaja-type asymptotic formulas are established for these operators. Finally, we consider graphical examples and their numerical interpretations to compare the speed of convergence for the composition operators and their components.
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Jordan n-derivations on alternative rings

26. April 2025

Ab Hamid Kawa, Shakir Ali, S. N. Hasan, Bilal Ahmad Wani

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In this paper, we investigate the problem of when a multiplicative Jordan n -derivation is additive in the case of alternative rings. More precisely, let ℛ {\mathscr{R}} be an alternative ring containing a non-trivial idempotent d 1 {d_{1}} and ℛ = ℛ 11 + ℛ 12 + ℛ 21 + ℛ 22 {\mathscr{R}=\mathscr{R}_{11}+\mathscr{R}_{12}+\mathscr{R}_{21}+\mathscr{R}_{2% 2}} , the Pierce decomposition of ℛ {\mathscr{R}} relative to d 1 {d_{1}} satisfies: (i) if ( d i ⁢ u ⁢ d j ) ⁢ z j ⁢ k = 0 {(d_{i}ud_{j})z_{jk}=0} for all z j ⁢ k ∈ ℛ j ⁢ k {z_{jk}\in\mathscr{R}_{jk}} , then ( d i ⁢ u ⁢ d j ) = 0 {(d_{i}ud_{j})=0} , (ii) if z i ⁢ j ⁢ ( d j ⁢ u ⁢ d k ) = 0 {z_{ij}(d_{j}ud_{k})=0} for all z i ⁢ j ∈ ℛ i ⁢ j {z_{ij}\in\mathscr{R}_{ij}} , then ( d j ⁢ u ⁢ d k ) = 0 {(d_{j}ud_{k})=0} , (iii) if ( d i ⁢ u ⁢ d i ) ⁢ z i ⁢ i + z i ⁢ i ⁢ ( d i ⁢ u ⁢ d i ) = 0 {(d_{i}ud_{i})z_{ii}+z_{ii}(d_{i}ud_{i})=0} for all z i ⁢ i ∈ ℛ i ⁢ i {z_{ii}\in\mathscr{R}_{ii}} , then ( d i ⁢ u ⁢ d i ) = 0 {(d_{i}ud_{i})=0} for i , j , k = 1 , 2 {i,j,k=1,2} . Further, if ξ is a mapping from ℛ {\mathscr{R}} into itself such that ξ is a multiplicative Jordan n -derivation, then ξ is additive. As a consequence of our main theorem, some known results can be either generalized or deduced. (cf. [8] and [9]).
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On the generating functions of products mixing two k-Fibonacci and other sequences

26. April 2025

Carlos M. da Fonseca

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We present a simple and general formula for the generating function of the product of two polynomial sequences, based on lesser-known results. This approach is largely of a matricial nature. We describe how to derive and simplify recent products involving the k -Fibonacci, k -Pell, and Chebyshev polynomials. Several relevant references are provided.
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q-Fibonacci statistical convergence

29. März 2025

Koray İbrahim Atabey, Muhammed Çınar, Mikail Et

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In this paper, we use the q -Fibonacci band matrix F ^ q = ( F ^ n ⁢ k ⁢ ( q ) ) {\widehat{F}_{q}=(\widehat{F}_{nk}(q))} to introduce the notions of q -Fibonacci summability, q -Fibonacci statistical convergence, strongly F ^ q ⁢ [ p ] {\widehat{F}_{q}[p]} -Cesàro summability and give some inclusion relations about these concepts.
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Matrix-weighted fractional type operators on spaces of homogeneous type

28. März 2025

Yuxun Zhang, Jiang Zhou

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In this paper, we introduce matrix A p , q {A_{p,q}} weights on spaces of homogeneous type in the sense of Coifman and Weiss, and prove some basic properties of these weights. As applications, the necessary and sufficient condition for the boundedness of matrix-weighted fractional maximal operators on Lebesgue spaces is established, and the boundedness of matrix-weighted fractional integral operators on Lebesgue spaces is obtained.
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Differential identities involving three generalized derivations on prime rings and Banach algebras

28. März 2025

Karim Bouchannafa, Abderrahman Hermas, Lahcen Oukhtite

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Let L be a non-central Lie ideal of a prime ring R . The primary objective of this paper is to characterize generalized derivations ℋ {\mathcal{H}} , ℱ {\mathcal{F}} and 𝒢 {\mathcal{G}} of R satisfying the following algebraic identity: x ⊥ ℋ ⁢ ( y ) = ℱ ⁢ ( x ) ⁢ y + y ⁢ 𝒢 ⁢ ( x ) for all ⁢ x , y ∈ L , x\bot\mathcal{H}(y)=\mathcal{F}(x)y+y\mathcal{G}(x)\quad\text{for all }x,y\in L, where ⊥ {\bot} represents either the Lie product [ ⋅ , ⋅ ] {[\,\cdot\,,\cdot\,]} , or the Jordan product ∘ {\circ} . Furthermore, we extend our results to Banach algebras.
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Nonoscillation theory of nonlinear differential equations of Emden–Fowler type with variable exponents

28. März 2025

Jaroslav Jaroš, Kusano Takaŝi

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We consider the Emden–Fowler differential equation with variable exponents and establish necessary, sufficient and both necessary and sufficient conditions for the existence of nonoscillatory solutions of this equation with three different patterns of asymptotic behavior at infinity. The Schauder–Tikhonov fixed point theorem and duality principle are used for this purpose.
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On the C-flat dimension of injective modules

28. März 2025

Ya-Nan Li, Zhaoyong Huang

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Let R and S be rings and let C S R {{}_{R}C_{S}} be a semidualizing bimodule. We investigate the behavior of the C -flat dimension of injective left R -modules, and establish the relation among the supremum of these C -flat dimensions and the supremum of C -injective dimensions of projective left S -modules and the supremum of C -projective dimensions of injective left R -modules.
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The heat equation for singular Dunkl–Laplacian operator

28. März 2025

Bayan Bekbolat, Niyaz Tokmagambetov

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The aim of this paper is to investigate the solvability of both direct and inverse problems related to the heat equation involving the Dunkl operator and Laplace operator in a punctured domain. We establish the existence and uniqueness of solutions for both classes of problems. Furthermore, explicit solution formulas for the problems under consideration are derived.
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On singular integral operators along surfaces

28. März 2025

Ahmad Al-Salman, Abdulla M. Jarrah

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Suppose that Ω ∈ L 1 ⁢ ( 𝕊 n - 1 × 𝕊 n - 1 ) {\Omega\in L^{1}(\mathbb{S}^{n-1}\times\mathbb{S}^{n-1})} is a homogeneous function of degree zero in the sense Ω ⁢ ( t ⁢ x , s ⁢ y ) = Ω ⁢ ( x , y ) for any ⁢ t , s > 0 \Omega(tx,sy)=\Omega(x,y)\quad\mbox{for any }t,s>0 satisfying the cancellation property ∫ 𝕊 n - 1 Ω ⁢ ( u , ⋅ ) ⁢ 𝑑 σ n ⁢ ( u ) = ∫ 𝕊 m - 1 Ω ⁢ ( ⋅ , v ) ⁢ 𝑑 σ m ⁢ ( v ) = 0 . \int_{\mathbb{S}^{n-1}}\Omega(u,\cdot\,)\,d\sigma_{n}(u)=\int_{\mathbb{S}^{m-1% }}\Omega(\,\cdot\,,v)\,d\sigma_{m}(v)=0. Under suitable growth conditions on the mappings ϕ 1 , ϕ 2 : ( 0 , ∞ ) → ℝ {\phi_{1},\phi_{2}:(0,\infty)\rightarrow\mathbb{R}} , we prove that the singular integral operator T Ω ( ϕ 1 ↫ ϕ 2 ) ⁢ ( f ) ⁢ ( x , y ) = p.v. ⁢ ∫ ℝ n × ℝ m f ⁢ ( ( x - ϕ 1 ⁢ ( | v | ) ⁢ u , y - ϕ 2 ⁢ ( | u | ) ⁢ v ) ) ⁢ Ω ⁢ ( u , v ) | u | n ⁢ | v | m ⁢ 𝑑 u ⁢ 𝑑 v T_{\Omega}^{(\phi_{1}\looparrowleft\phi_{2})}(f)(x,y)=\textup{p.v.}\int_{% \mathbb{R}^{n}\times\mathbb{R}^{m}}f((x-\phi_{1}(|v|)u,y-\phi_{2}(|u|)v))\frac% {\Omega(u,v)}{|u|^{n}|v|^{m}}\,du\,dv is bounded on L p ⁢ ( ℝ n × ℝ m ) {L^{p}(\mathbb{R}^{n}\times\mathbb{R}^{m})} , 1 < p < ∞ {1<p<\infty} , provided the kernel function Ω satisfies weak size conditions. Furthermore, we prove the boundedness of the related truncated maximal singular integral operators.
Open Access
On generating properties of the weak commutativity of p-groups, p odd

2. März 2025

Raimundo Bastos, Ricardo de Oliveira, Nathália Gonçalves, Carmine Monetta

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In the present paper, we examine the generating properties of Sidki’s weak commutativity group. More precisely, if G and G φ {G^{\varphi}} are two isomorphic groups, the weak commutativity group χ ⁢ ( G ) {\chi(G)} is the group generated by G and G φ {G^{\varphi}} subject to the relations [ g , g φ ] = 1 {[g,g^{\varphi}]=1} for all g ∈ G {g\in G} . Here we provide bounds for the number of generators of some subgroups of χ ⁢ ( G ) {\chi(G)} when G is a p -group of odd order and either G is powerful or D ⁢ ( G ) {D(G)} is abelian.
Open Access
Fibrations of classifying spaces in the simplicial setting

25. Februar 2025

Matthias Franz

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In this note we show that in the simplicial setting, the classifying space construction converts short exact sequences of groups not just to homotopy fibrations, but in fact to fibre bundles.
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Asymptotic behavior of impulsive parabolic problem with infinite-dimensional impulsive set

23. Februar 2025

Oleksiy Kapustyan, Juliya Fedorenko, Svetlana Temesheva

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In the paper we consider semilinear parabolic equation with a nonlinear term ε ⁢ f ⁢ ( u ) {\varepsilon f(u)} , whose trajectories undergo impulsive perturbations when they meet the impulsive set M = { ∥ u ∥ = R } {M=\{\|u\|=R\}} . We prove that for sufficiently small ε this problem generates an impulsive dynamical system which possesses a compact uniform attractor in the phase space L 2 {L^{2}} .
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New results on exponential stability of time-varying systems using logarithmic norm

21. Februar 2025

Mekki Hammi

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This work is concerned with the stability analysis of nonlinear time-varying systems by using a generalized integral inequality of Gamidov type. The approach is based on the use of the notion of logarithmic norm. We give sufficient conditions for exponential stability of the perturbed system, including Lyapunov-type stability criteria and eigenvalue conditions on “slowly varying systems”. The effectiveness of the proposed approach is illustrated by numerical examples.
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Action of higher derivations on prime rings with involution

21. Februar 2025

Shakir Ali, Amal S. Alali, Vaishali Varshney, Naira Noor Rafiquee

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In this paper, we monitor the behavior of a prime ring with involution of second kind. Such rings are studied through the prism of higher derivations satisfying certain differential identities. Precisely, we prove that for a higher derivation D = ( d i ) i ∈ ℕ ∪ { 0 } {D=(d_{i})_{i\in\mathbb{N}\cup\{{0}\}}} , if we are able to establish the identity, d n ⁢ [ x , x * ] ∈ Z ⁢ ( R ) {d_{n}[x,x^{*}]\in Z(R)} for a single positive integer n , then the structure exhibits certain interesting properties. Some similar looking results are also presented.
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When every finitely generated regular ideal is principal

21. Februar 2025

Mohamed Chhiti, Salah Eddine Mahdou

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In this paper, we introduce a ring in which every finitely generated regular ideal is principal, and we call it a regular Bézout ring. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated duplication of a ring along an ideal. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.
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Continuity property of pseudodifferential operators from the weak Hardy spaces to the weak Lebesgue space

21. Februar 2025

Yu-Long Deng

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This paper discusses the boundedness of pseudodifferential operator on weak Hardy space and provides a sufficient condition such that the operator is continuous from the weak Hardy space into the weak Lebesgue space.
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3D quadratic ODE systems with hidden oscillations

11. Februar 2025

Yongjun Li, Eduard Musafirov, Alexander Grin, Andrei Pranevich

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An autonomous three-dimensional quadratic system of ordinary differential equations with two parameters is considered. This system exhibits hidden oscillations at certain parameter values (it has a limit cycle, but does not have equilibrium points). We are looking for non-autonomous perturbations of this autonomous system that do not change the Mironenko reflecting function. Such so-called admissible perturbations preserve some qualitative properties of the solutions of the original system. For perturbed non-autonomous systems, we derived the Lyapunov stability of equilibrium solutions, proved the existence of the limit cycle and periodic solutions, as well as their stability (instability).
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Some spectral properties of left and right generalized Fredholm operators

10. Februar 2025

Abdelhalim Azzouz, Mahamed Beghdadi, Bilel Krichen

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The scope of this paper is to introduce and study new classes of operators, namely, left and right generalized Fredholm operators. We also investigate the spectrum of left and right generalized Fredholm and generalized Weyl operators. At the end of the work, the invariance of the left (right) generalized Fredholm and generalized Weyl spectra is studied.
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One-sided extended g-Drazin inverses

10. Februar 2025

Dijana Mosić

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The principal goal of this paper is to present one-sided versions of the extended g -Drazin inverse as weaker kinds of the extended g -Drazin inverse. Precisely, we define left and right extended g -Drazin inverses for Banach algebra elements. A number of characterizations for left and right extended g -Drazin inverses are developed. Since we obtain equivalence between concepts of left (or right) extended g -Drazin invertibility and left (or right) generalized Drazin invertibility, in fact, we get new characterizations for left (or right) generalized Drazin invertibility as consequences. As particular cases of one-sided extended g -Drazin inverses, we investigate one-sided extended Drazin inverses.
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Propagation of waves from finite sources arranged in line segments within an infinite triangular lattice

10. Februar 2025

David Kapanadze, Zurab Vashakidze

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This paper examines the propagation of time-harmonic waves in a two-dimensional triangular lattice with a lattice constant a = 1 {a=1} . The sources are positioned along line segments within the lattice. Specifically, we investigate the discrete Helmholtz equation with a wavenumber k ∈ ( 0 , 2 ⁢ 2 ) {k\in(0,2\sqrt{2})} , where input data is prescribed on finite rows or columns of lattice sites. We focus on two main questions: the efficacy of the numerical methods employed in evaluating the Green’s function, and the necessity of the cone condition. Consistent with a continuum theory, we employ the notion of radiating solution and establish a unique solvability result and Green’s representation formula using difference potentials. Finally, we propose a numerical computation method and demonstrate its efficiency through examples related to the propagation problems in the left-handed two-dimensional inductor-capacitor metamaterial.

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Editor-in-Chief
Ivan Kiguradze
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
Email: gmj-rmi@tsu.ge

Executive Editor
Tengiz Buchukuri
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
E-mail: t_buchukuri@yahoo.com

Editorial Secretary
Maia Kvinikadze
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
Email: maia.kvinikadze@tsu.ge

Editorial Board
Hans-Joachim Baues
Max-Planck-Institut für Mathematik
53072 Bonn, Germany
Email: baues@mpim-bonn.mpg.de

Oleg V. Besov
Steklov Mathematical Institute
Russian Acad. Sciences
119991 Moscow, Russia

Pavel Drábek
Department of Mathematics and NTIS
Faculty of Applied Sciences
University of West Bohemia
Univerzitní 8, 301 00 Plzeň
Czech Republic
Email: pdrabek@kma.zcu.cz

Roland Duduchava
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
Email: dudu@rmi.ge

Lasha Ephremidze
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
Email: lasha@rmi.ge

Revaz Gamkrelidze
Steklov Mathematical Institute
Russian Acad. Sciences
119991 Moscow, Russia
Email: gam@ips.ras.ru

Hvedri Inassaridze
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
Email: hvedri@rmi.ge

Mamuka Jibladze
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
Email: jib@rmi.ge

Tornike Kadeishvili
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia

Email: kade@rmi.ge

Otto Helmut Kegel
Institut für Mathematik
Albert-Ludwigs-Universität
79104 Freiburg, Germany
Email: otto.h.kegel@math.uni-freiburg.de

Alexander Kharazishvili
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
Email: kharaz2@yahoo.com

Sergo Kharibegashvili
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
Email: kharibegashvili@yahoo.com

Estate Khmaladze
School of Mathematics, Statistics and Operations Research
Victoria University
Wellington 6140, New Zealand
Email: estate.khmaladze@msor.vuw.ac.nz

Tariel Kiguradze
Department of Mathematical Sciences
Florida Institute of Technology
Melbourne, FL 32901-6975, U.S.A.
Email: tkigurad@fit.edu

Samuel Krushkal
Dept. of Mathematics and Computer Science
Bar-Ilan University 52900
Ramat Gan, Israel
Email: krushkal@macs.biu.ac.il

Stanislaw Kwapien
Institute of Mathematics
Warsaw University
02-097 Warsaw, Poland
Email: kwapstan@mimuw.edu.pl

Hans Rudolf Lerche
Institut f. Math. Stochastik
Albert-Ludwigs-Universität
79104 Freiburg, Germany
Email: lerche@stochastik.uni-freiburg.de

Michael Mania
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia
Email: misha.mania@gmail.com

Jean Mawhin
Institut de Mathematique Pure et Appliquee
Universite Catholique de Louvain
1348 Louvain-la-Neuve, Belgium
Email: jean.mawhin@uclouvain.be

Alexander Meskhi
A. Razmadze Mathematical Institute
I. Javakhishvili Tbilisi State University
2, Merab Aleksidze II Lane
0193 Tbilisi, Georgia

Paolo Emilio Ricci
Dipartimento di Matematica "Guido Castelnuovo"
Universita degli Studi di Roma "La Sapienza"
00185 Roma, Italy
Email: paoloemilioricci@gmail.com

Vaja Tarieladze
N. Muskhelishvili Inst. Comput. Math.
Georgian Technical University
0171 Tbilisi, Georgia
Email: vajatarieladze@yahoo.com

Hans Triebel
Mathematisches Institut
Fr.-Schiller-Universität Jena
07743 Jena, Germany
Email: hans.triebel@uni-jena.de

Fabio Zanolin
Dept. of Mathematics and Computer Science
University of Udine
Via delle Science 6
33100 Udine, Italy
Email: fabio.zanolin@dimi.uniud.it

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Mathematik Mathematik, Allgemeines

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1572-9176

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1072-947X

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Erstveröffentlichung:

1. Februar 1994

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6 Hefte pro Jahr

eISSN: 1572-9176

ISSN: 1072-947X

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