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Zeitschrift

Journal of Applied Analysis

Editors-in-Chief: Włodzimierz Fechner und Krzysztof Ciesielski
Managing Editor: Leslaw Gajek

Sprache: Englisch

Erstveröffentlichung: 1. Juni 1995

Erscheinungsweise: 2 Hefte pro Jahr

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Über diese Zeitschrift

Objective
Journal of Applied Analysis is an international journal devoted to applications of mathematical analysis. Among them there are applications to economics (in particular finance and insurance), mathematical physics, mechanics and computer sciences. The journal also welcomes works showing connections between mathematical analysis and other domains of mathematics such as geometry, topology, logic and set theory.

The journal is jointly produced by the Institute of Mathematics of the Technical University of Łódź and De Gruyter.

Topics
Topics include:

applications of mathematical analysis (real and complex, harmonic, convex, variational)
differential equations
dynamical systems
optimization (linear, nonlinear, convex, nonsmooth, multicriterial)
optimal control
stochastic modeling and probability theory
numerical methods

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Research articles

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Autocontinuity, strict convergence in measure and convergence of integral sequences

29. August 2025

Do Huy Hoang, Truong Thi Nhan, Dao Van Duong, Tran Nhat Luan

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In this paper, we give an alternative proof for the proof of Theorem 2.23 shown in the paper [J. Borzová-Molnárová, L. Halčinová and O. Hutník, The smallest semicopula-based universal integrals II: Convergence theorems, Fuzzy Sets and Systems 271 2015, 18–30] by exploiting the uniform continuity of the underlying semicopula together with using ε-techniques of limit. Thus, our proof avoids using the way interchanging the supremum and infimum which is not valid in general.
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Statistical Riemann and Lebesgue integrability by deferred Cesàro and deferred Nörlund mean and Korovkin’s theorem

29. August 2025

Sanjeev Verma, Kavita Saini, Kuldip Raj, Mohammad Mursaleen

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The current work focuses on statistical Riemann summability, statistical Riemann integrability, statistical Lebesgue summability, and statistical Lebesgue integrability using Deferred Cesàro and Deferred Nörlund means. First, we explore key theorems that connect these concepts, providing examples for illustration. In our newly established sequence spaces, we illustrate the application of Korovkin-type approximation theorems, supported by some examples of positive linear operators showcasing the significance of our results.
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From the Zakharov system to the NLS equation on the torus

9. Juli 2025

Raphael Taraca, Guido Schneider

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The NLS equation can be derived from the Zakharov system in a singular limit. The goal of this paper is to add some new aspects to the existing analysis about this approximation. We outline the differences between the situation x ∈ ℝ {x\in{\mathbb{R}}} and x ∈ 𝕋 = ℝ / ( 2 ⁢ π ⁢ ℤ ) {x\in\mathbb{T}={\mathbb{R}}/(2\pi{\mathbb{Z}})} . We explain the difficulties occurring in the construction of higher order approximations and use these approximations to improve the approximation rate. Moreover, we point out that the standard validity proof requires a smallness condition which was not stated in the existing literature.
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Almost periodic-type functions and their applications: Survey of recent results and further perspectives

9. Juli 2025

Marko Kostić

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In this paper, we present a brief survey of recent results about various classes of almost periodic-type functions and their applications to the abstract Volterra integro-differential equations, nonlinear evolution equations of first order, ordinary differential equations and some classes of integro-differential-difference equations. We consider the Poincaré–Perron problem for higher-order ordinary differential equations in the class of almost periodic-type functions and the almost periodic points and minimal sets in ω-regular spaces, among many other interesting topics, providing also some perspectives for expanding the theory of almost periodic functions.
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Equilibria for abstract economies with convex or acyclic valued correspondences

25. Juni 2025

Donal O’Regan

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Using collectively fixed point theorems, we establish new equilibrium results for abstract economies where the constraint and preference correspondences are Kakutani or acyclic maps. First we present a variety of new collectively fixed point theorems based on a generalized Schauder type theorem. This then enables us to establish new equilibrium results for abstract economies where, in particular, we obtain new general results for acyclic valued constraint and preference correspondences.
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Young’s inequality for orthonormal systems

17. Juni 2025

Arup Kumar Maity

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We have demonstrated Young’s inequality for an orthonormal system for twisted convolution setup. As an application, we show some new Fourier multipliers.
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On duals of certain types of sequence spaces of complex uncertain variable

29. Mai 2025

Birojit Das, Binod Chandra Tripathy, Ömer Kisi, Carlos Granados

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Uncertainty theory has significantly advanced and expanded over the past ten years. In this article, we introduce the notions of uncertain α-dual, uncertain β-dual and uncertain γ-dual of complex uncertain sequence spaces. Convergence and boundedness of complex uncertain sequences are taken in the sense of almost surely due to B. Liu and then few characterizations of the newly introduced uncertain dual spaces are established. Furthermore, our goal is to propose and establish inclusion relations within these sequence spaces.
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Monotone traveling wave solutions of Mackey–Glass reaction diffusion equation with delayed diffusion term

29. Mai 2025

William Kyle Barker, Nguyen Truong Thanh, Nguyen Van Minh

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This work investigates the existence of solutions to the Mackey–Glass equation, incorporating delays in both the diffusion and birth functions. This equation, a nonlinear functional differential equation, plays a significant role in modeling phenomena in biology and physiology. Using the monotone iteration method, we construct quasi-upper and quasi-lower solutions to rigorously establish the existence of solutions. The analysis relies on a modified Perron’s theorem.
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On representations of mean-field variational inference

28. März 2025

Soumyadip Ghosh, Yingdong Lu, Tomasz Nowicki, Edith Zhang

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Variational Bayes has allowed the analysis of Bayes’ rule in terms of gradient flows, partial differential equations (PDE), and diffusion processes. Mean-field variational inference (MFVI) is a version of approximate Bayesian inference that optimizes over product distributions. In the spirit of variational Bayes, we represent the MFVI problem in three different manners: a gradient flow in a Wasserstein space, a system of quasilinear PDE, and a McKean–Vlasov diffusion process. Furthermore, we show that a time-discretized coordinate ascent variational inference algorithm in the product Wasserstein space of measures yields a gradient flow in the small-time-step limit. A similar result is obtained for their associated densities, with the limit given by a system of quasilinear PDEs. We illustrate how the tools provided here can be used to guarantee convergence of algorithms, and can be extended to a variety of approaches, old and new, to solve MFVI problems.
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Expanding Legendre polynomials

1. März 2025

Rafael Ferraro

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The expansion of Legendre polynomials P ℓ ⁢ ( cos ⁡ θ ) {P_{\ell}(\cos\theta)} in cosines of multiples of θ is obtained by comparing the 2 ℓ {2^{\ell}} -pole solution of Laplace equation in complex coordinates with its usual form in spherical coordinates.
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Renormalization bi-Heyting algebra

25. Januar 2025

Ali Shojaei-Fard

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We formulate a bi-Heyting algebra structure on the space of Feynman diagrams of a quantum field theory. This particular bi-Heyting algebra, which is originated from Feynman graphon representations of 1PI Green’s functions together with renormalization and core coproducts, provides some new topological treatments for the study of the asymptotics of 1PI Green’s functions and their corrections.
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Second Titchmarsh's theorem for the generalized Fourier transform in the space L^p(dμ_{k, n})

13. Januar 2025

Mohamed El Hamma, Abdessalam Chablaoui, Radouan Daher

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Using a translation operator, we obtain a generalization of second Titchmarsh’s theorem for the ( k , n ) {(k,n)} -generalized Fourier transform for functions satisfying the ( p , k , n ) (p,k,n) -Lipschitz and ( ψ , k , n ) (\psi,k,n) -Lipschitz classes condition in the space L p ⁢ ( d ⁢ μ k , n ) {\mathrm{L}^{p}(d\mu_{k,n})} , where 1 ≤ p ≤ 2 {1\leq p\leq 2} .
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Lie symmetries, exact solutions and conservation laws of (2+1)-dimensional time fractional cubic Schrödinger equation

2. Oktober 2024

Jicheng Yu, Yuqiang Feng

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In this paper, Lie symmetry analysis method is applied to ( 2 + 1 ) {(2+1)} -dimensional time fractional cubic Schrödinger equation. We obtain all the Lie symmetries and reduce the ( 2 + 1 ) {(2+1)} -dimensional fractional partial differential equations with Riemann–Liouville fractional derivative to ( 1 + 1 ) (1+1) -dimensional counterparts with Erdélyi–Kober fractional derivative. Then we obtain the power series solutions of the reduced equations and prove their convergence. In addition, the conservation laws for the governing model are constructed by the new conservation theorem and the generalization of Noether operators.
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Analysis of a nonlinear elliptic system with variable coefficients and Hardy potential with Carathéodory nonlinearity: Existence

2. Oktober 2024

Khaled Kefi, Qiguang An, Jian Liu

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This study investigates existence result of a nontrivial weak solutions for a system of nonlinear elliptic equations involving Hardy Potentials. The problem arises in the mathematical modeling of complex physical phenomena.
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Heat equation for Sturm–Liouville operator with singular propagation and potential

2. Oktober 2024

Michael Ruzhansky, Alibek Yeskermessuly

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This article considers the initial boundary value problem for the heat equation with the time-dependent Sturm–Liouville operator with singular potentials. To obtain a solution by the method of separation of variables, the problem is reduced to the problem of eigenvalues of the Sturm–Liouville operator. Further on, the solution to the initial boundary value problem is constructed in the form of a Fourier series expansion. A heterogeneous case is also considered. Finally, we establish the well-posedness of the equation in the case when the potential and initial data are distributions, also for singular time-dependent coefficients.
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Static perfect fluid spacetime on Riemannian manifolds admitting concurrent-recurrent vector field with Bach tensor

3. September 2024

M. M. Praveena, Aruna Kumara H., C. M. Arjun, M. S. Siddesha

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In this paper, we first consider the 𝕊 ⁢ ℙ ⁢ 𝔽 {\mathbb{SPF}} equation on a Riemannian CRVF-manifold M and show that either M is Einstein or the potential function is pointwise collinear with ζ on an open set U of M . Next, we show that if a Riemannian CRVF-manifold M is the spatial factor of a 𝕊 ⁢ ℙ ⁢ 𝔽 {\mathbb{SPF}} with a Batch tensor then it is a Batch flat space-time manifold.
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On the existence, uniqueness and regularity of strong solutions to a stochastic 2D Cahn–Hilliard-Magnetohydrodynamic model

3. September 2024

Calvin Tadmon, Gabriel Deugoué, Salvador Awo Kougang

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We investigate a stochastic coupled model of the Cahn–Hilliard equations and the stochastic magnetohydrodynamic equations in a bounded domain of ℝ 2 {\mathbb{R}^{2}} . The model describes the flow of the mixture of two incompressible and immiscible fluids under the influence of an electromagnetic field with stochastic perturbations. We prove the existence, uniqueness and regularity of a probabilistic strong solution. The proof of the existence is based on the Galerkin approximation, the stopping time technique and some weak convergence principles in functional analysis.
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Anisotropic obstacle Neumann problems in weighted Sobolev spaces and variable exponent

3. September 2024

Ghizlane Zineddaine, Abdelaziz Sabiry, Said Melliani, Abderrazak Kassidi

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In this paper we focus on a certain class of anisotropic obstacle problems governed by a Leray–Lions operator. This problem is subject to homogeneous Neumann boundary conditions. By applying truncation techniques and the monotonicity method, we establish the existence of entropy solutions for the problem studied in the framework of anisotropic weighted Sobolev spaces with variable exponent.
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Degree of approximation of functions conjugate to the functions belonging to Lip((𝜉₁,𝜉₂)𝑟)-class through double Nörlund means

6. August 2024

Shailesh Kumar Srivastava, Shivani Luhar, Sachin Devaiya

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In this paper, we determine the error of approximation of functions, conjugate to the functions of two variables ( 2 ⁢ π 2\pi -periodic in both variables) belonging to the Lipschitz class Lip ( ( ξ 1 , ξ 2 ) ; r \operatorname{Lip}((\xi_{1},\xi_{2});r ) ( r ≥ 1 r\geq 1 ), through the double Nörlund means of its conjugate double Fourier series. Additionally, in the form of corollaries, we present some particular cases of the theorem proved here.
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Some classification of affine homothetical surfaces of finite type in 𝕀

3. August 2024

Bendehiba Senoussi

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A Euclidean submanifold is said to be of Chen finite type if its coordinate functions are a finite sum of eigenfunctions of its Laplacian Δ. In this paper, we classify two types of affine homothetical surfaces of finite type in isotropic 3-space 𝕀 3 {\mathbb{I}^{3}} under the condition Δ ⁢ r i = λ i ⁢ r i {\Delta r_{i}=\lambda_{i}r_{i}} , where ( r i ) {(r_{i})} is the i -component function of the position vector r ( i = 1 , 2 , 3 {i=1,2,3} ), λ i ∈ ℝ {\lambda_{i}\in\mathbb{R}} and Δ denotes the Laplace operator.
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Some results on Kenmotsu space forms

1. Januar 2000

Shanmukha B, Suhad Ali Osman Abdallah, N. S. Abd El-Gawaad

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The object of the present paper is to study Kenmotsu space forms satisfying pseudosymmetric, Ricci-pseudosymmetric and locally-ϕ-symmetric. Further we study the quasi-conformal flat and quasi-conformal semisymmetric Kenmotsu space forms.
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Study of nonlinear PDE with power nonlinearities

1. Januar 2000

Alexander G. Ramm

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Let u ′ + A ⁢ u = h ⁢ ( u , t ) + f ⁢ ( x , t ) {u^{\prime}+Au=h(u,t)+f(x,t)} , u ⁢ ( x , 0 ) = u 0 ⁢ ( x ) {u(x,0)=u_{0}(x)} , where u ∈ H {u\in H} , u ′ := u t := d ⁢ u d ⁢ t {u^{\prime}:=u_{t}:=\frac{du}{dt}} , H is a Hilbert space, ∥ h ⁢ ( u , t ) ∥ ≤ a ⁢ ∥ u ∥ p ⁢ ( 1 + t ) - b \|h(u,t)\|\leq a\|u\|^{p}(1+t)^{-b} , ( A ⁢ u , u ) ≥ γ ⁢ ( t ) ⁢ ( u , u ) {(Au,u)\geq\gamma(t)(u,u)} , γ ⁢ ( t ) = c ⁢ ( 1 + t ) - c 1 {\gamma(t)=c(1+t)^{-c_{1}}} . Here p , a , b , c , c 1 {p,a,b,c,c_{1}} are positive constants. Sufficient conditions are given for the above problem to have a solution bounded or going to zero as t → ∞ {t\to\infty} .
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Some aspects of 𝜆-weak convergence using difference operator

1. Januar 2000

Archana Sharma, Reena Kumari, Vijay Kumar

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In this paper, we introduce generalized difference weak sequence space classes by utilizing the difference operator Δ ı ȷ \Delta^{\jmath}_{\imath} and the de la Vallée–Poussin mean, denoted as [ ( V , λ ) w , Δ ı ȷ ] m [(\mathscr{V},\lambda)_{w},\Delta^{\jmath}_{\imath}]_{m} for m = 0 m=0 , 1, and ∞. Further, we explore some algebraic and topological properties of these spaces, including their nature as linear, normed, Banach, and BK spaces. Additionally, we examine properties such as solidity, symmetry, and monotonicity. Finally, we define and establish some inclusion relations among generalized difference weak statistical convergence, generalized difference weak 𝜆-statistical convergence, and generalized difference weak [ V , λ ] [\mathscr{V},\lambda] -convergence.
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A geometry in the set of solutions to ill-posed linear problems with box constraints: Applications to probabilities on discrete sets

1. Januar 2000

Henryk Gzyl

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When there are no constraints upon the solutions of the equation 𝑨 ⁢ 𝝃 = 𝒚 {{\boldsymbol{A}}{\boldsymbol{\xi}}={\boldsymbol{y}}} , where 𝑨 {{\boldsymbol{A}}} is a K × N - {K\times N-} matrix, 𝝃 ∈ ℝ N {{\boldsymbol{\xi}}\in{\mathbb{R}}^{N}} and 𝒚 ∈ ℝ K {{\boldsymbol{y}}\in{\mathbb{R}}^{K}} a given vector, the description of the set of solutions as 𝒚 {{\boldsymbol{y}}} varies in ℝ K {{\mathbb{R}}^{K}} is well known. But this is not so when the solutions are required to satisfy 𝝃 ∈ 𝒦 ⁢ ∏ i ≤ j ≤ N [ a j , b j ] {{\boldsymbol{\xi}}\in{\mathcal{K}}\prod_{i\leq j\leq N}[a_{j},b_{j}]} , for finite a j ≤ b j : 1 ≤ j ≤ N {a_{j}\leq b_{j}:1\leq j\leq N} . To solve this problem we bring in a strictly convex, Fermi-Dirac entropy function Ψ ⁢ ( 𝝃 ) {\Psi({\boldsymbol{\xi}})} , and find the solution as a ⁢ r ⁢ g ⁢ m ⁢ i ⁢ n ⁢ { Ψ ⁢ ( 𝝃 ) : 𝝃 ∈ 𝒦 , 𝑨 ⁢ 𝝃 = y } {argmin\{\Psi({\boldsymbol{\xi}}):{\boldsymbol{\xi}}\in{\mathcal{K}},\,{% \boldsymbol{A}}{\boldsymbol{\xi}}=y\}} . If λ denotes the Lagrange multipliers of the optimization problem, we study the properties of the parametric surface 𝝀 → 𝝃 ⁢ ( 𝝀 ) {{\boldsymbol{\lambda}}\to{\boldsymbol{\xi}}({\boldsymbol{\lambda}})} in the geometry on 𝒦 {{\mathcal{K}}} defined by the Hessian metric derived from Ψ ⁢ ( 𝝃 ) {\Psi({\boldsymbol{\xi}})} . In particular, we prove that the surface 𝝀 → 𝝃 ⁢ ( 𝝀 ) {{\boldsymbol{\lambda}}\to{\boldsymbol{\xi}}({\boldsymbol{\lambda}})} is contained in ker ( 𝑨 ) ⊥ {\ker({\boldsymbol{A}})^{\perp}} in the Hessian metric derived from Ψ.
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Positive solutions for a class of singular fractional boundary value problem with p-Laplacian

1. Januar 2000

Saroj Panigrahi, Raghvendra Kumar

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In this paper, an attempt has been made to establish the sufficient conditions for the existence and multiplicity of positive solutions by using the fixed point index theory and the Avery–Peterson fixed point theorem respectively for the following class of nonlinear singular fractional differential equation D 0 + β ⁢ ( ϕ p ⁢ ( D 0 + α ⁢ u ⁢ ( t ) ) ) + f ⁢ ( t , u ⁢ ( t ) , … , u ( n - 2 ) ⁢ ( t ) ) = 0 , t ∈ ( 0 , 1 ) , D_{0^{+}}^{\beta}(\phi_{p}(D_{0^{+}}^{\alpha}u(t)))+f(t,u(t),\dots,u^{(n-2)}(t% ))=0,\quad t\in(0,1), with the boundary conditions u ( k ) ⁢ ( 0 ) = 0 , 0 ≤ k ≤ n - 2 , D 0 + α ⁢ u ⁢ ( 0 ) = 0 , D 0 + α - 1 ⁢ u ⁢ ( 1 ) = ∫ 0 1 D 0 + α - 1 ⁢ u ⁢ ( t ) ⁢ 𝑑 A ⁢ ( t ) , u^{(k)}(0)=0,\quad 0\leq k\leq n-2,\qquad D_{0^{+}}^{\alpha}u(0)=0,\qquad D_{0% ^{+}}^{\alpha-1}u(1)=\int_{0}^{1}D_{0^{+}}^{\alpha-1}u(t)\,dA(t), where 0 < β ≤ 1 {0<\beta\leq 1} , n - 1 < α ≤ n {n-1<\alpha\leq n} , n ≥ 3 {n\geq 3} , A : [ 0 , 1 ] → ℝ {A:[0,1]\to\mathbb{R}} is a function of bounded variation, ϕ p ⁢ ( s ) = | s | p - 2 ⁢ s {\phi_{p}(s)=|s|^{p-2}s} for p > 1 {p>1} and ϕ q ⁢ ( s ) {\phi_{q}(s)} is the inverse of ϕ p ⁢ ( s ) {\phi_{p}(s)} , where p , q {p,q} satisfies the relation 1 p + 1 q = 1 {\frac{1}{p}+\frac{1}{q}=1} , f may have singularity at t = 0 {t=0} .
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Estimations of Levinson-type inequalities using novel 3-convex Green functions with Taylor’s formula

1. Januar 2000

Awais Rasheed, Khuram Ali Khan, Josip Pečarić, Đilda Pečarić

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The goal of this study is to derive the generalized Levinson-type inequalities in the form of Taylor representation for higher order convex functions. This study uses Taylor’s formula and several novel types of 3-convex Green functions, to establish the novel identities associated with Bullen-type inequalities for higher order convex functions. Moreover, various Levinson-type inequalities are proved for positive real weights using Green functions and Taylor’s formula.
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Uncertainty principles for the Dunkl–Weinstein–Stockwell transform

1. Januar 2000

Fethi Soltani, Ibrahim Maktouf

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In this paper, we prove a Heisenberg uncertainty inequality and a local uncertainty inequality for the Dunkl–Weinstein–Stockwell transform. We give also a Shapiro-type uncertainty inequality for this transform.
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Some improvements on the convergence in measure for sequence of semicopula-based universal integrals

1. Januar 2000

Do Huy Hoang, Truong Thi Nhan, Dao Van Duong, Tran Nhat Luan

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In this paper, we study an improvement on convergence in the measure theorem of a sequence of seminormed fuzzy integrals which has been proposed by Xuecheng. Furthermore, some other forms of convergence in measure are also presented.
Open Access
A functional equation for monomial functions

1. Januar 2000

Eszter Gselmann, Mehak Iqbal

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Let F ⊂ K \mathbb{F}\subset\mathbb{K} be fields with characteristic zero, 𝑛 a positive integer and κ ∈ K \kappa\in\mathbb{K} . In this paper, we determine those monomials f : F → K f\colon\mathbb{F}\to\mathbb{K} of degree 𝑛 for which f ⁢ ( x 2 ) = κ ⋅ x n ⁢ f ⁢ ( x ) f(x^{2})=\kappa\cdot x^{n}f(x) holds for all x ∈ F x\in\mathbb{F} . We show that, similar to the classical results, where additive functions were considered, the monomial functions in the equation can be represented with the aid of homomorphisms and higher-order derivations.
Open Access
Proportional population models and stability analysis on time scales

1. Januar 2000

Ayşe Çiğdem Yar, Emrah Yilmaz

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The study of changes in population size and reasons for these changes appear as population dynamics. These dynamics generally focus on change in population size over time. Mathematical modeling is used to make sense of these changes. In this study, three population models have been reconstructed and solved using proportional derivative on time scales. Equilibrium points and stability states of these solutions were examined.
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W-distance based ϕ-coupled fixed point problem: Solution, well-posedness and applications to integral and functional equations

1. Januar 2000

Subhadip Roy, Binayak S. Choudhury, Parbati Saha

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In this paper we solve a fixed point problem formulated through a combination of three different contemporary trends in fixed point theory, namely, φ-fixed point results, coupled fixed point results and the use of w -distances. We have cited examples to illustrate our main theorem and to demonstrate how our theorem generalizes some known theorems and augments the domain of applicability of our result to a larger family of functions compared to these previous results. Well-posedness property of the problem is established. In a separate section we discuss two different applications of our result to problems of integral equations and functional equations.
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Existence of solutions for a q-fractional p-Laplacian SIR model

1. Januar 2000

Achraf Zinihi, Moulay Rchid Sidi Ammi, Ahmed Bachir, Pradip Debnath

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This paper presents an existence result for a novel nonlinear Caputo q -fractional p -Laplacian epidemiological model on time scales. The proof of the main result leverages Arzelà–Ascoli and Schauder’s fixed point theorems. Additionally, a set of open questions is addressed to further enrich this field of valuable scientific research
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Parametric inequalities involving fractional integrals with exponential kernels

1. Januar 2000

Wedad Saleh, Badreddine Meftah, Hüseyin Budak, Abdelghani Lakhdari

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This paper explores integral inequalities within the framework of fractional integrals having exponential kernels through a parameterized approach. A novel integral identity with a parameter is introduced, forming the basis for deriving a general inequality. From this, several classical inequalities, including midpoint, trapezium, Bullen, Simpson, and corrected Simpson types, are obtained for differentiable convex functions. Numerical examples and graphical analyses are presented to verify the validity of the proposed results. The findings are further demonstrated through applications to special functions, showcasing the versatility of the developed framework.
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A family of polylogarithmic integrals

1. Januar 2000

Anthony Sofo, Jean-Christophe Pain, Victor Scharaschkin

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In this paper we investigate a class of integrals that were encountered in the course of a work on statistical plasma physics, in the so-called Sommerfeld temperature-expansion of the electronic entropy. We show that such integrals, involving some parameters, can be fully described in closed form represented by special functions.
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Toeplitz operators associated with the Whittaker Gabor transform and applications

1. Januar 2000

Hatem Mejjaoli

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The Whittaker Gabor transform (WGT) is a novel addition to the class of Gabor transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short span of time. Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, the aim of this article is to explore two more aspects of the time-frequency analysis associated with the WGT including the spectral analysis associated with the concentration operators and the scalogram.
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Shift dynamical systems and remotely almost periodic functions

1. Januar 2000

David Cheban

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The purpose of this work is to study remotely almost periodic functions defined on the semi-axis ℝ + := [ 0 , + ∞ ) {\mathbb{R}_{+}:=[0,+\infty)} (respectively, on the real axis ℝ := ( - ∞ , + ∞ ) {\mathbb{R}:=(-\infty,+\infty)} ) with values in the Banach space 𝔅 {\mathfrak{B}} . We establish a relation between remotely almost periodic movements in the shift dynamical system ( C ( 𝕋 , 𝔅 ) , 𝕋 {(C(\mathbb{T},\mathfrak{B}),\mathbb{T}} , σ ) {\sigma)} ( 𝕋 = ℝ + {\mathbb{T}=\mathbb{R}_{+}} or ℝ {\mathbb{R}} ) in the space of continuous functions C ⁢ ( 𝕋 , 𝔅 ) C(\mathbb{T},\mathfrak{B}) and remotely almost periodic functions. Using this connection, we prove some important analytical and topological properties of remotely almost periodic functions.
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On the Cowling approximation: A verification of ansatz via methods of functional and asymptotic analysis

1. Januar 2000

Christopher J. Winfield

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We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic degree and high oscillation frequency. Our methods involve a reformulation of the system in terms of an integro-differential equation for which certain Hilbert-space methods apply. By way of a more complete asymptotic study, we extend our results to certain fundamental solution sets, characterized according to certain multi-point boundary-value problems: Such asymptotics further enable us to produce sharp estimates as confirmation of our general results.
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On Egorov-like theorems for monotone measure

1. Januar 2000

Do Huy Hoang, Truong Thi Nhan, Pham Thanh Son, Dao Van Duong, Tran Nhat Luan

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In theory of generalized measure, Egorov-like theorems have been investigated. In this article, we introduce generalized concepts of almost everywhere convergence and almost uniform convergence. Next Egorov-like theorems with respect to the generalized convergences are provided. Finally, versions of Egorov condition for the more general context of convergence are also established.

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Editors-in-Chief
Włodzimierz Fechner
Insitute of Mathematics
Technical University of Lódz
Wólczanska 215
90-924 Lódz, Poland
E-mail: wlodzimierz.fechner@p.lodz.pl

Krzysztof Ciesielski
Mathematics Department
West Virginia University
Morgantown, WV 26506-6310, USA
E-mail: jaa@math.wvu.edu

Managing Editor
Leslaw Gajek
Institute of Mathematics
Technical University of Lódz
Wólczanska 215
93-005 Lódz, Poland
E-mail: gal@p.lodz.pl

Editorial Board Assistant
Żywilla Fechner
Institute of Mathematics
Technical University of Lódz
Wólczanska 215
90-924 Lódz, Poland
E-mail: jaa@info.p.lodz.pl

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Qamrul Hasan Ansari
Department of Mathematics
Aligarh Muslim University
Aligarh 202 002, India
E-mail: qhansari@gmail.com

Jan Awrejcewicz
Department of Automatics and Biomechanics
Technical University of Lódz
Stefanowskiego 1/15
90-924 Lódz, Poland
E-mail: awrejcew@p.lodz.pl

Philippe Biane
Laboratoire d'Informatique
Institut Gaspard Monge
Université de Marne la Vallée
77454 Marne-la-Vallée cedex 2, France
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Michel Chipot
Institut für Mathematik
Universität Zürich
8057 Zürich, Switzerland
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Udayan B. Darji
Department of Mathematics
University of Louisville
Louisville, KY 40292, USA
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Silvestru Sever Dragomir
School of Engineering and Science
Victoria University
Melbourne VIC 8001, Australia
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Celso Grebogi
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School of Natural and Computing Sciences
King’s College
University of Aberdeen
Old Aberdeen AB24 3UE, UK
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Ryszard Jajte
Faculty of Mathematics and Computer Science
University of Lódz
S. Banacha 22
90-238 Lódz, Poland
E-mail: rjajte@math.uni.lodz.pl

Alexander Kharazishvili
A. Razmadze Institute of Mathematics
Georgian Academy of Sciences
380093 Tbilisi, Georgia
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Sándor Komlósi
Faculty of Business and Economics
Janus Pannonius University
7622, Pécs, Hungary
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J. Martin Lindsay
Department of Mathematics and Statistics
Lancaster University
Lancaster LA1 4YF, UK
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Andrzej Luczak
Faculty of Mathematics and Computer Science
University of Lódz
S. Banacha 22
90-238 Lódz, Poland
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Zhi-Ming Ma
Institute of Applied Mathematics, CAS
Academy of Mathematics and Systems Science
Beijing 100190, China
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Janusz Matkowski
Faculty of Mathematics, Computer Science and Econometrics
Prof. Z Szafrana 4a
65-516 Zielona Góra, Poland
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Boris Mordukhovich
Department of Mathematics
Wayne State University
Detroit, MI 48202, USA
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Eszter Novák-Gselmann
Institute of Mathematics
Faculty of Science and Technology
University of Debrecen
H-4032 Debrecen
Egyetem tér 1, Hungary
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Andrzej Nowakowski
Faculty of Mathematics and Computer Science
University of Lódz
S. Banacha 22
90-238 Lódz, Poland
E-mail: annowako@math.uni.lodz.pl

Alexander Olevskii
School of Mathematical Sciences
Tel Aviv University
Ramat Aviv 69978, Israel
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Simeon Reich
Department of Mathematics
Technion Israel Institute of Technology
32000 Haifa, Israel
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R. Tyrrell Rockafellar
Department of Mathematics
University of Washington
Seattle, WA 98195-4350, USA
E-mail: rtr@math.washington.edu

Saharon Shelah
Einstein Institute of Mathematics
The Hebrew University of Jerusalem
Givat Ram, 91904 Jerusalem, Israel
and
Department of Mathematics
Rutgers University
New Brunswick, Piscataway NJ 08854, USA
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Yoshihiro Shibata
Department of Mathematical Sciences
School of Science and Engineering
Waseda University
Shinjyuku-ku, Tokyo 169-8555, Japan
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Hari M. Srivastava
Department of Mathematics and Statistics
University of Victoria
Victoria, British Columbia V8W 3R4, Canada
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Laszlo Szekelyhidi
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University of Debrecen
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Lionel Thibault
Département Mathématiques
Université Montpellier II
Place Eugène Bataillon
34095 Montpellier cedex 5, France
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Wladyslaw Wilczynski
Faculty of Mathematics and Computer Science
University of Lódz
S. Banacha 22
90-238 Lódz, Poland
E-mail: wwil@uni.lodz.pl

Hong-Kun Xu
Hangzhou Dianzi University Hangzhou, China
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Dariusz Zagrodny
Faculty of Mathematics and Computer Science
University of Lodz
Banacha 22
90-238 Łódź, Poland
E-mail: dariusz.zagrodny@wmii.uni.lodz.pl

Wojciech Zajaczkowski
Institute of Mathematics and Cryptology
Cybernetics Faculty
Military University of Technology
Kaliskiego 2
00-908 Warsaw, Poland
and
Institute of Mathematics
Polish Academy of Sciences
Sniadeckich 8
00-956 Warsaw, Poland
E-mail: wz@impan.gov.pl

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eISSN: 1869-6082

ISSN: 1425-6908

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