Volume 73, Issue 1

In the paper, the authors present the Schur m -power convexity and concavity for the general geometric Bonferroni mean of multiple parameters and establish comparison inequalities for bounding the general geometric Bonferroni mean in terms of the arithmetic, geometric, and harmonic means. These Schur convexity and concavity provide a unified generalization of the Schur convexity and concavity for the geometric Bonferroni means of two or three parameters.

It is elementary and well known that if an element x of a bounded modular lattice L $ \mathbf L $ has a complement in L $ \mathbf L $ then x has a relative complement in every interval [ a , b ] containing x . We show that the relatively strong assumption of modularity of L $ \mathbf L $ can be replaced by a weaker one formulated in the language of so-called modular triples. We further show that, in general, we need not suppose that x has a complement in L $ \mathbf L $ . By introducing the concept of modular triples in posets, we extend our results obtained for lattices to posets. It should be remarked that the notion of a complement can be introduced also in posets that are not bounded.

An MV-algebra A is radically principal if every prime ideal P of A is radically principal, i.e., there exists a principal ideal I of A such that Rad ( P ) = Rad ( I ) $ \text{Rad}(P)=\text{Rad}(I) $ . We investigate radically principal MV-algebras and provide some characterizations as well as some classes of examples. We prove a Cohen-like theorem, precisely, an MV-algebra is radically principal if and only if every maximal ideal is radically principal. It is also shown that the radically principal hyperarchemedian MV-algebras are the weakly finite ones and the radically principal Boolean algebras are the finite ones. Radically principal MV-algebras are also studied from the perspective of lattice-ordered groups.

In this paper, a Stone-type duality for directed complete posets with a top element is developed by using a class of special subsets, named prime Scott open subsets. Following this idea, a topological duality for complete lattices is also obtained.

Let { P n } n ⩾0 be the Padovan sequence with initial conditions P 0 =0, P 1 =1, and P 2 =1 and the recurrence relation P n +3 = P n +1 + P n . Its companion sequence is known as the Perrin sequence { E n } n ⩾0 that satisfies the same above recurrence relation with the initial conditions E 0 =3, E 1 =0 and E 2 =2. In this paper, we determine all Padovan and Perrin numbers that are concatenations of two distinct base b repdigits with 2 ⩽ b ⩽ 9. As corollary, we prove that the largest Padovan and Perrin numbers which can be representable as a concatenations of two distinct base b repdigits are P26=816=2244‾7 $ P_{26}=816=\overline{2244}_7 $ and E24=853=31111‾4 $ E_{24}=853=\overline{31111}_4 $ .

Let G be a group of order n and H be a subgroup of order m of G . Denote by ψ H ( G ) the sum of element orders relative to H of G . It is known that if G is nilpotent, then ψH(G)≤ψHm(Cn) $ \psi_H(G) \leq\psi_{H_m}(C_n) $ , where H m is the unique subgroup of order m of C n . In this note, we show that this inequality does not hold for infinitely many finite solvable groups.

In this paper, we define new classes of functions related to metrics and w -distances. We also provide characterizations of functions in these classes. As a consequence, we obtain relations between all classes.

In [ Logarithmic coefficient bounds and coefficient conjectures for classes associated with convex functions , J. Funct. Spaces 2021 (2021), Art. ID 6690027], Alimohammadi et al. presented a few conjectures for the logarithmic coefficients γ n of the functions f belonging to some well-known classes like C(1+αz) $ \mathcal{C}(1+\alpha z) $ for α  ∈ (0, 1], and CVhpl(1/2) $ \mathcal{CV}_{hpl}(1/2) $ . For example, it is conjectured that if the function f∈C(1+αz) $ f\in\mathcal{C}(1+\alpha z) $ , then the logarithmic coefficients of f satisfy the inequalities |γn|≤α2n(n+1),n∈N. $$ |\gamma_n|\le\dfrac{\alpha}{2n(n+1)},\quad n\in\mathbb{N}. $$ Equality is attained for the function L α , n , that is, logLα,n(z)z=2∑n=1∞γn(Lα,n)zn=αn(n+1)zn+…,z∈U. $$ \log\dfrac{L_{\alpha,n}(z)}{z}=2\sum\limits_{n=1}^{\infty}{\gamma_n(L_{\alpha,n})z^n} =\frac{\alpha}{n(n+1)}z^n+\dots,\quad z\in\mathbb{U}. $$ The aim of this paper is to confirm that these conjectures hold for the coefficient γ n 0 −1 whenever the function f has the form f(z)=z+∑k=n0∞akzk $ f(z)=z+\sum\limits_{k=n_{0}}^{\infty}{a_kz^k} $ , z∈U $ z\in\mathbb{U} $ for some n0∈N $ n_0\in\mathbb{N} $ , n 0 ⩾2.

In this paper, multiple periodic solutions are obtained for second-order Hamiltonian systems with ( q , p )-Laplacian when the nonlinearity is partially periodic. New results are deduced by using minimax principle via critical point theory.

In this paper, by using Sadovskii’s fixed point theorem and the properties of the measure of noncompactness, we establish some sufficient conditions for the asymptotic stability results of nonlinear neutral integro-differential equations with variable delays. The results presented in this paper improve and generalize some results in the literature. An example is considered to illustrate our main results.

The introduction of notion of regular matrix to act as a summability method has proved to be an impeccable tool in analysing the convergence of the otherwise non–convergent sequences. One such intriguing matrix namely Catalan matrix operator was initiated and studied in the settings of sequence spaces by Kara and Kara [ Matrix transformations and compact operators on Catalan sequence spaces , J. Math. Anal. Appl. 498 (1) (2001)]. In addition to studying their convergence in the setting of usual norm, a generalized version of the norm called fuzzy norm was introduced. This article explores the ideal convergence of sequences via Catalan matrix operator and fuzzy norm. Novel corresponding sequence spaces have been constructed, several interesting properties of the spaces have been studied and parallels have been drawn with some pre-existing notions. The research further explores algebraic and toplogical properties of the spaces.

In this paper we prove pointwise and distributional Fourier transform inversion theorems for functions on the real line that are locally of bounded variation, while in a neighbourhood of infinity are Lebesgue integrable or have polynomial growth. We also allow the Fourier transform to exist in the principal value sense. A function is called regulated if it has a left limit and a right limit at each point. The main inversion theorem is obtained by solving the differential equation df(t)−iωf(t)=g(t) $ {\text{d}} f(t)-\text{i}\omega f(t)=g(t) $ for a regulated function f , where ω is a complex number with positive imaginary part. This is done using the Henstock–Stieltjes integral. This is an integral defined with Riemann sums and a gauge. Some variants of the integration by parts formula are also proved for this integral. When the function is of polynomial growth its Fourier transform exists in a distributional sense, although the inversion formula only involves integration of functions and returns pointwise values.

The purpose of this article is to study the notionof approximate numerical radius orthogonality in semi-Hilbertian structure. Given a positive operator A on a Hilbert space H $ \mathbb{H} $ , we introduce the notion of ( ε , A )-approximate numerical radius orthogonality for A -bounded operators and characterize it. The results obtained here generalize all the existing notions of numerical radius orthogonality. Furthermore, for a fixed θ  ∈ [0, 2 π ), we introduce the notion of numerical radius derivative DwAθ(T,S) $ D^\theta_{w_A}(T,S) $ of an A -bounded operator T in the direction of another A -bounded operator S and obtain a relation between DwAθ(T,S) $ D^\theta_{w_A}(T,S) $ and ( ε , A )-approximate numerical radius orthogonality.

Our goal is to define new classes of bounded linear operators between two Hilbert spaces, solving corresponding systems of equations. Precisely, we introduce the Wg-Drazin-star operator and its dual, extending the notions of the W -weighted Drazin-star matrix and its dual for a rectangular matrix. We prove many characterizations and operator matrix representations of the Wg-Drazin-star operator and its dual. As special cases of the Wg-Drazin-star operator and its dual, the g-Drazin-star operator and its dual are presented and studied. Applying our new classes of operators, we also solve adequate equations. Thus, we generalize some well-known results and present new results.

The Lupaş q -transform comes out naturally in the study of the Lupaş q -analogue of the Bernstein operator. It is closely related to the Heine q -distribution which has a numerous application in q -boson operator calculus and to the Valiron method of summation for divergent series. In this paper, the Lupaş q -transform (Λ q f )( z ), q  ∈ (0, 1), of unbounded functions is considered in distinction to the previous researches, where only the case f  ∈  C [0, 1] have been investigated. First, the condition for a function to possess the Lupaş q -transform is presented. Also, results concerning the connection between growth rate of the function f ( t ) as t  → 1 − and the growth of its Lupaş q -transform (Λ q f )( z ) as z  → ∞ are established.

Using generalized Pohozaev-Schoen integral identity, we prove that a compact K -contact manifold of dimension >3 $ \gt 3 $ admitting a proper η -Ricci almost soliton is isometric to a unit sphere S 2 n +1 provided its scalar curvature is constant. Next, it is proved that if a ( k , μ )-contact metric represents a non-trivial gradient generalized η -Ricci soliton, then M is flat in dimension 3 and in higher dimensions M is either η -Einstein or locally isometric to E n +1  ×  S n (4).

Ideal convergence of subsequence is defined in such a way that every subsequence of an ideal convergent sequence is ideal convergent which enabled to introduce 𝓘 -compactness and 𝓘* -compactness of topological spaces meaningfully. The penetration of 𝓘 -nonthin subsequences gives rise to these twin concepts of compactness which are different from usual compactness even in metric spaces in general.

In the present paper, we study a generalized allocation scheme and establish some asymptotic properties for the number of cells containing a given number of particles in the scheme, which include law of large numbers, central limit theorem, moderate deviation principle, and Hoeffding type inequality. These results generalize the work of Chuprunov and Fazekas [ An analogue of a generalized allocation scheme: limit theorems for the number of cells of a given size , Discrete Math. Appl. 22 (1) (2012), 101–122].

In this article, a new flexible distribution called shifted generalized truncated Nadarajah-Haghighi (SGeTNH) distribution is generalized from the Nadarajah-Haghighi distribution. The hazard rate function of SGeTNH distribution is very flexible and can be increasing, decreasing, bathtub-shaped, upside-down bathtub-shaped, depending on the parameter values. Estimations of parameters of the proposed distribution are derived based on the alternative maximum likelihood estimation (AMLE), least squares estimation (LSE), and Cramér-von Mises estimation (CVME) methods. Monte Carlo simulations are performed to show the accuracy of the proposed methods of estimations. Several real data sets on cancer deaths and COVID-19 daily mortality are applied to illustrate the flexibility and usefulness of SGeTNH distribution for modeling reliability data.

The aim of this paper is to consider the extropy measure of uncertainty proposed by Lad, Sanfilippo and Agrò for the problem of compressive sensing. For this purpose, two sampling designs, i.e., simple random sampling (SRS) and a modified version of ranked set sampling, known as maximum ranked set sampling procedure with unequal samples (MRSSU), are utilized and some uncertainty measures such as extropy, cumulative extropy and residual extropy are obtained and compared for these sampling designs. Also, some results of extropy in record ranked set sampling data are developed. Then a study on comparing the behavior of estimators of cumulative extropy in MRSSU and SRS using simulation method is obtained. As an example, two sampling methods MRSSU and SRS are utilized for compressive sensing technique and their performances are compared via signal to noise ratio (SNR), correlation coefficient of reconstructed and the original signal and cumulative extropy measure of uncertainty. The results show that the values of SNR and correlation coefficient for MRSSU are higher than those of SRS. Furthermore, it is shown that MRSSU scheme can efficiently reduce the uncertainty measure of cumulative extropy.

Let Hn+(R) $ H_{n}^{+}(\mathbb{R}) $ be the cone of all positive semidefinite n  ×  n real matrices. We describe the form of all surjective maps on Hn+(R) $ H_{n}^{+}(\mathbb{R}) $ , n =3, that preserve the star partial order in both directions.