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Georgian Mathematical Journal

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Editorial Board: , , , , , , , , , , , , , , , , , , , , , , , , , and

Language: English

First published: February 1, 1994

Publication Frequency: 6 issues per year

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1.7 CiteScore
0.24 MCQ
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About this journal

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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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all fields of pure and applied mathematics

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As of 2026, all De Gruyter journal subscriptions include access to every issue, from Volume 1, Issue 1 through to today, meaning subscribers can access even more research at no additional cost.

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Gyro-L^p spaces

October 23, 2026

Lorenzo Matarazzo

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In this paper we introduce a gyro-analogue of L p spaces; we achieve this goal by constructing normed gyrolinear structures on the set of functions from an arbitrary measure space to the Möbius gyrovector space ℳ s and the Einstein gyrovector space ℰ s . This gives rise to two major classes of gyro- L p spaces: Möbius s - L p gyrospaces and Einstein s - L p gyrospaces. These two spaces will form a normed gyrolinear space with respect to the ∥ ⋅ ∥ p ℳ s gyronorm and the ∥ ⋅ ∥ p ℰ s gyronorm, respectively. We show that the Einstein L p -gyrospaces and Möbius L p -gyrospaces are isomorphic, and the isomorphism between them also preserves the L p gyronorm, thus giving rise to a gyroisometry. Furthermore, we show that the Möbius and Einstein L p gyronorms induce a complete metric space structure on the Möbius L p gyrospace and the Einstein L p gyrospace, respectively.
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Mixed-type dynamical interaction problem of acoustic waves and thermo-electro-magneto-elastic solids

October 23, 2026

George Chkadua

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In the paper, we consider a three-dimensional dynamical model of fluid-solid interaction in which a generalized thermo-electro-magneto-elastic body occupying a bounded region Ω + is embedded in an inviscid fluid occupying an unbounded domain Ω - = ℝ 3 ∖ Ω + ¯ . In this case, we have a six-dimensional Green–Lindsay’s model of the generalized dynamical thermo-electro-magneto-elastic field (consisting of the displacement vector with three components, electric potential, magnetic potential, and temperature distribution function) in the domain Ω + , while we have a scalar acoustic pressure field in the unbounded domain Ω - . The physical kinematic and dynamic relations are described mathematically by appropriate boundary and transmission conditions. Using the Laplace transform, the dynamical interaction mixed-type problem is reduced to the corresponding interaction problem for elliptic pseudo-oscillation equations containing a complex parameter τ. We derive the appropriate norm estimates with respect to the complex parameter τ and construct the solution of the original dynamical mixed-type problem by the inverse Laplace transform. As a result, we prove the uniqueness and existence of a solution for the dynamical interaction mixed-type problem.
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Nonlinear mixed right Jordan and left bi-skew Jordan-type derivations on *-algebra

October 23, 2026

Amal S. Alali, Md Arshad Madni, Muzibur Rahman Mozumder

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Let 𝔄 be a unital ∗ -algebra over the complex field ℂ . In this work, we prove that, under suitable conditions, every nonlinear mixed right Jordan and left bi-skew Jordan n -derivation is an additive ∗ -derivation. The applicability of the main result is further illustrated through its extension to various significant special cases of unital ∗ -algebras, namely prime ∗ -algebras and factor von Neumann algebras.
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Existence and multiplicity of solutions for nonlocal fourth-order p(x)-Kirchhoff problems with Leray--Lions operators, Hardy potentials, and logarithmic nonlinearities

October 23, 2026

Salah Boulaaras

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This paper is devoted to the existence and multiplicity of weak solutions for a class of nonlocal fourth-order p ⁢ ( x ) -Kirchhoff problems involving a Leray–Lions type operator, Hardy-type singular potentials, and logarithmic nonlinear reaction terms in the framework of variable exponent Sobolev spaces. More precisely, we investigate the boundary value problem geändert { M ⁢ ( ∫ Ω A ⁢ ( x , Δ ⁢ u ) ⁢ 𝑑 x ) ⁢ Δ ⁢ ( a ⁢ ( x , Δ ⁢ u ) ) + θ ⁢ ( x ) ⁢ | u | s ⁢ ( x ) - 2 ⁢ u | x | 2 ⁢ s ⁢ ( x ) + c ⁢ ( x ) ⁢ | u | q ⁢ ( x ) - 2 ⁢ u = λ ⁢ f ⁢ ( x , u ) + μ ⁢ g ⁢ ( x , u ) + β ⁢ | u | r ⁢ ( x ) - 2 ⁢ u ⁢ ln ⁡ ( 1 + | u | ) , in ⁢ Ω , u = Δ ⁢ u = 0 , on ⁢ ∂ ⁡ Ω , see text where Ω ⊂ ℝ N ( N ≥ 2 ) is a bounded domain with smooth boundary, M is a nonlocal Kirchhoff function, a ⁢ ( x , ⋅ ) is a Leray–Lions type operator satisfying suitable structural assumptions, and the singular weighted term | u | s ⁢ ( x ) - 2 ⁢ u | x | 2 ⁢ s ⁢ ( x ) represents a Hardy-type potential. The additional logarithmic perturbation β ⁢ | u | r ⁢ ( x ) - 2 ⁢ u ⁢ ln ⁡ ( 1 + | u | ) models a broad class of nonlinear reaction mechanisms exhibiting intermediate growth between polynomial and super-polynomial nonlinearities. The nonlinearities f and g satisfy suitable Carathéodory conditions, while λ > 0 , μ ≥ 0 , and β ≥ 0 are real parameters. Using variational methods, compact embedding theorems in variable exponent Sobolev spaces, Hardy–Rellich inequalities, monotonicity techniques associated with Leray–Lions operators, and the Three Critical Points Theorems of Bonanno–Marano and Bonanno–Candito, we establish the existence of at least three distinct weak solutions. The presence of the logarithmic reaction term requires a refined variational analysis owing to its nonhomogeneous growth and the delicate compactness properties arising in variable exponent settings. The obtained results significantly generalize and unify several existing multiplicity theorems for fourth-order p ⁢ ( x ) -Kirchhoff and p ⁢ ( x ) -biharmonic problems by simultaneously incorporating nonlocal Kirchhoff effects, Leray–Lions structures, Hardy-type singular potentials, variable exponent logarithmic nonlinearities, and additional nonlinear perturbations within a unified variational framework. To the best of our knowledge, this paper provides one of the first multiplicity results for nonlocal fourth-order variable exponent Kirchhoff problems combining all these features in a single mathematical model.
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A completeness theorem on the boundary in Besov spaces

October 23, 2026

Alberto Cialdea, Carmine Sebastiano Mare, David Natroshvili

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Let { ω k } be a basis of polynomial solutions to the equation E ⁢ u = 0 , where E is a higher-order elliptic operator with real constant coefficients and no lower-order terms, in any number of variables. The aim of the paper is to prove that the system { ( ω k , ∂ ν ⁡ ω k , … , ∂ ν m - 1 ⁡ ω k ) } is complete in the Besov space [ B p , p 1 - 1 / p ⁢ ( ∂ ⁡ Ω ) ] m ( 1 ≤ p < ∞ ) , Ω being a C ∞ bounded domain in ℝ n such that ℝ n ∖ Ω ¯ is connected.
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Characterizations of normal matrices using the group inverse and the Moore–Penrose inverse

October 23, 2026

Xiaoli Li, Lanping Zhu, Qianglian Huang, Junchao Wei

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This paper presents a systematic study of the characterization of normal matrices through the properties of products involving their generalized inverses. A series of necessary and sufficient conditions characterizing normal matrices has been established from multiple perspectives, including one-sided Hermitian nature, one-sided equalities, X -commutativity, classical commutativity conditions, the existence of solutions to associated matrix equations, and the explicit forms of the general solutions to these equations.
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Polynomial differentiation composition operators from the minimal Möbius invariant space into Zygmund-type spaces

October 23, 2026

Zhitao Guo

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We characterize the boundedness and compactness of the polynomial differentiation composition operator P ψ → , φ n from the minimal Möbius invariant space ℬ 1 to the Zygmund-type space 𝒵 μ and its little subspace 𝒵 μ , 0 . Using derivative estimates and test functions in ℬ 1 , we obtain explicit necessary and sufficient conditions for boundedness, along with asymptotic estimates for the operator norm. We further establish complete compactness criteria. These results complement and improve upon recent studies in this direction.
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Generalized symmetric bi-derivations on posets

October 23, 2026

Ahmed Y. Abdelwanis, Shakir Ali, Vaishali Varshney

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The key objective of the present paper is to initiate the study of generalized symmetric bi-derivations on posets. Additionally, several characterization theorems for generalized symmetric bi-derivations are given. Moreover, the properties of the fixed points based on the generalized symmetric bi-derivations are examined. Finally, the properties of ideals and operations related to generalized symmetric bi-derivations are studied.
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Approximating solutions of fractional differential equations via a new faster iteration scheme in hyperbolic spaces

October 23, 2026

Yunus Atalan, Ertan Gündoğdu

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In this paper, we introduce a new four-step fixed point iteration scheme in the framework of hyperbolic spaces as defined by Kohlenbach. We establish strong convergence theorems for the proposed iteration scheme for contractive-like mappings having a fixed point. Furthermore, we present a detailed rate analysis and prove that explicit error majorants for our iteration decay faster than those for the Abbas–Nazir iteration under suitable control-parameter assumptions. For positive affine contractions, this comparison also applies to actual errors. We also establish a data dependence result for the new scheme. Finally, we illustrate the theoretical findings through numerical examples and an application to a fractional differential equation. The examples show fewer iteration cycles at stated tolerances; iteration counts, operator-evaluation costs, and discretization errors are distinguished.
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Maximal operator on L ^p(·) spaces over spaces of homogeneous type: Local boundedness

October 23, 2026

Tengiz Kopaliani, Alina Shalukhina, George Tephnadze

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We prove the local boundedness of the Hardy–Littlewood maximal operator on variable Lebesgue spaces L p ⁢ ( ⋅ ) ⁢ ( X ) over spaces of homogeneous type for exponents p ⁢ ( ⋅ ) which are bounded away from 1 and ∞ and satisfy a local Muckenhoupt condition 𝒜 loc ⁢ ( X ) . This generalizes a Euclidean theorem of A. K. Lerner. Our proof utilizes the machinery of adjacent dyadic grids.
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Stability for a wave equation with fractional structural damping subjected to an internal distributed delay

October 23, 2026

Manal Alotaibi, Nasser-Eddine Tatar, Waled Al-Khulaifi

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In this paper, we investigate the exponential stability of a wave equation in a bounded domain with fractional structural damping and an internal distributed time delay. The damping mechanism is modeled by a spectral fractional Laplacian ( - Δ ) α with α ∈ ( 0 , 1 ) , while the delay is described by a convolution term acting on the velocity. By extending a delay-absorption technique to the genuinely fractional regime, we reformulate the system and construct an appropriate Lyapunov functional. Under explicit conditions linking the damping parameter and the size of the delay kernel, we establish exponential decay of the energy. The result quantifies the dominance relationship between fractional dissipation and memory effects, thereby filling the gap between the classical damping case ( α = 0 ) and the strongly damped case ( α = 1 ) .
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A note on twisted Cartesian products with base a sphere

September 30, 2026

Juan Antonio Delgado

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We prove that, for a twisted Cartesian product S m × τ F with base a sphere, the corresponding twisted tensor product C ⁢ ( S m ) ⊗ t C ⁢ ( F ) induced by the Twisted Eilenberg–Zilber Theorem can be endowed with a differential graded coalgebra structure. Furthermore, we show that the corresponding injection C ⁢ ( S m ) ⊗ t C ⁢ ( F ) → C ⁢ ( S m × τ F ) reduces to the Eilenberg–Mac Lane shuffle map while preserving the condition of morphism of differential graded coalgebras. These computations allow us to explicitly exhibit the differences and resemblances with respect to Szczarba’s approach to the study of fibre bundles.
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On Carathéodory theorem for open discrete unclosed mappings

August 26, 2026

Zarina Kovba, Evgeny Sevost’yanov

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We study mappings satisfying the inverse Poletsky-type inequality in a domain of the Euclidean space. Such inequalities are well known and play an important role in the study of quasiconformal and quasiregular mappings. We consider the case when the mapped domain, generally speaking, is not locally connected on its boundary. At the same time, we consider the situation when the mapping is open and discrete, but may not preserve the boundary of the domain. In terms of prime ends, we obtain results on the equicontinuity of families of such mappings in the closure of the definition domain. As a consequence, we also obtain the corresponding statement for Orlicz–Sobolev classes.
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Two rare sets in a category base with an absolutely non-Baire sum

August 26, 2026

Sanjib Basu, Abhit Chandra Pramanik, Navdeep Tamang

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In this paper, we give generalized versions (in category bases) of two results of Kharazishvili, the second one dealing with absolute nonmeasurability of Minkowski’s sum of two universal measure zero sets with respect to the completion of any non-zero, σ -finite, Borel measure. Both results were based on an earlier result of Erdös, Kunen and Mauldin.
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Existence of three weak solutions for a fractional problem with logarithmic nonlinearity involving the ψ-Hilfer operator

August 26, 2026

Salah Boulaaras, Abdelaziz Sabiry

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In this paper, we study a nonlinear fractional boundary value problem involving a p -Laplacian-type ψ-Hilfer operator with a logarithmic source term under homogeneous Dirichlet boundary conditions in a one-dimensional domain Ω ⊂ ℝ . The logarithmic nonlinearity introduces slow-growth effects and additional analytical difficulties compared to standard polynomial-type nonlinearities. Using a variational framework, we associate the problem with an energy functional defined on a suitable Banach space (which is reflexive) and establish its main properties, including coercivity and the Palais–Smale condition. By applying the Bonanno–Marano-type three critical points theorem, we prove the existence of at least three distinct weak solutions. The results extend previous works in the ψ-Hilfer setting by explicitly treating logarithmic nonlinearities and highlighting the differences with existing polynomial-growth models.
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New characterizations of weak CMP inverses

August 26, 2026

Shuxian Xu, Jianlong Chen

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In 2025, Mosić defined the weak CMP inverse utilizing a minimal rank weak Drazin inverse instead of the Drazin inverse. The weak CMP inverse is a new broader class of generalized inverses, with the CMP and MPCEP inverses as particular cases, and it has applications in solving systems of linear equations. In this paper, we provide several expressions, along with a number of new characterizations and properties of the weak CMP inverse by means of Hartwig–Spindelböck decomposition. Moreover, we investigate the relationships between the weak CMP inverse and some well-known generalized inverses, such as the Moore–Penrose inverse and the weak MPD inverse. Finally, we show that the weak CMP inverse, weak MPD inverse and weak DMP inverse are all strong Bott–Duffin ( e , f ) -inverses.
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Rough ideal statistical convergence for complex uncertain double sequences

August 26, 2026

Nesar Hossain, Ayhan Esi

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In this paper, we introduce the notion of rough ℐ 2 -statistical convergence (denoted as r ⁢ - ⁢ 𝒮 ⁢ ( ℐ 2 ) -convergence) of complex uncertain double sequences in four fundamental aspects of uncertainty, namely almost sure, measure, mean, and distribution. This framework extends the existing notion of rough ℐ -convergence for complex uncertain sequences to the broader setting of double sequences. In addition, we investigate r ⁢ - ⁢ 𝒮 ⁢ ( ℐ 2 ) -convergence in p -distance and r ⁢ - ⁢ 𝒮 ⁢ ( ℐ 2 ) -convergence in metric for complex uncertain double sequences. Overall, this study provides a comprehensive diagrammatic illustration of the interrelationships among the various r ⁢ - ⁢ 𝒮 ⁢ ( ℐ 2 ) -convergence concepts and offers some significant observations highlighting their distinctions, supported by illustrative examples.
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Applications of selection theorems to multi-valued relatively nonexpansive mappings in hyperconvex spaces

July 30, 2026

Moosa Gabeleh, Jack T. Markin

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Building upon earlier work by the present authors on the existence of best proximity points (pairs) for single-valued cyclic and noncyclic relatively nonexpansive mappings in hyperconvex spaces, we study broader classes of multi-valued relatively nonexpansive and relatively u-continuous mappings in the setting of hyperconvex metric spaces. By developing appropriate selection theorems, we establish new and more general existence results for best proximity points and pairs, which significantly extend and refine the well-known results of Kirk, Reich, and Veeramani on proximinal retracts and best proximity pairs. In addition, by employing a suitable measure of noncompactness, we obtain extensions of the classical Sadovskiĭ fixed point theorem to both cyclic and noncyclic frameworks, thereby unifying and strengthening several existing results in the literature.
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Hilbert’s inequality in several variables

July 30, 2026

Gholamreza Talebi

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The s -dimensional discrete and continuous Hilbert operators are introduced, extending the classical Hilbert inequality to several variables. Through an inductive argument, it is shown that in both cases the p -norm of the operator equals ( π ⁢ csc ⁡ ( π p ) ) s , with the constant being optimal. The proofs rely on the factorization of the multi-dimensional kernel and the sharp one-dimensional inequality.
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Advancing joint B-Weyl operators: Stability and spectral extensions in Banach spaces

July 29, 2026

Aymen Bahloul, Ines Walha

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In this paper, we introduce and investigate new classes of d -tuples of operators on Banach spaces, namely, the joint left and joint right B-Weyl operators. These notions represent a significant advancement in the study of d -tuples of operators and extend the recent work initiated in [A. Bahloul, Insights into a new class of unbounded operators, Georgian Math. J. 32 2025, 2, 211–218], by generalizing the concepts of left and right B-Weyl operators. Our approach focuses on analyzing the stability of these new classes under finite-rank and commuting quasi-nilpotent perturbations, thereby demonstrating their robustness in broader contexts. Furthermore, we establish novel spectral characterizations linking joint B-Weyl spectra to joint Drazin spectra. These results deepen the understanding of multivariable operator theory and extend classical results of B-Fredholm theory to the joint setting of left and right B-Weyl spectra.
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Further results on modularity in evolution algebras

July 29, 2026

Manuel Ladra, Andrés Pérez-Rodríguez

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In this paper, we study modularity in the context of evolution algebras. Although this property has been previously considered, a complete description is still missing in several natural settings. In particular, we obtain a full characterization of modular evolution algebras in the nilpotent case and in the class of supersolvable regular evolution algebras.
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A new sequence of approximation operators involving modified Bessel functions of first kind

July 29, 2026

Vijay Gupta, Carmen-Violeta Popescu (Muraru), Ardeleanu Elena Roxana, Marcelina Mocanu

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The present article deals with an approximation operator, which is based on the modified Bessel function of the first kind. Such operators are linear positive operators and preserve only the constant functions among the power test functions. We construct these operators by a partial differential equation (PDE). Also, a more general form based on two parameters is captured from the PDE. We establish some direct approximation results and, in addition, consider the composition of these operators with Szász–Mirakyan operators, which provide us with another new operator, which is based on generalized Laguerre polynomials. We also estimate the approximation process for the new composite operator.
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Coefficient problems for the classes connected with a lune-shaped domain

July 29, 2026

Sanju Mandal, Molla Basir Ahamed, Paweł Zaprawa

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The study of coefficient problems in geometric function theory has a rich history. The challenging and interesting task is to determine sharp bounds for various inequalities related to different classes of univalent functions. In this article, we derive sharp bounds for the Hankel determinant involving logarithmic coefficients, the Zalcman functional J 2 , 3 := a 2 ⁢ a 3 - a 4 , the Fekete–Szegö inequality and the moduli differences of the logarithmic coefficients as well as the logarithmic coefficients of the inverse function for the classes 𝒮 ☾ * and 𝒞 ☾ , respectively.
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Approximation of Lipschitz functions by sampling operators

June 25, 2026

Borislav R. Draganov

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We establish a characterization of the rate of approximation of the generalized sampling operator for Lipschitz functions. Our primary goal is to weaken assumptions on the kernel of the sampling operator in order to be able to cover cases to which the already known general theorems are not applicable. In particular, we consider sampling operators generated by the Fejér kernel and low-order Bochner–Riesz kernels.
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Reduced quaternionic Cauchy-like integrals

June 25, 2026

Isidro Paulino-Basurto, Juan Bory-Reyes, José Oscar González-Cervantes, Baruch Schneider

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The works of the Swiss mathematician Karl Rudolf Fueter and the Romanian mathematicians Grigore Constantin Moisil and Nicolae Victor Teodorescu marked the starting point of a hypercomplex analysis over the skew field of real quaternions. Nowadays, this function theory, so-called quaternionic analysis, is the most attractive and close generalization of complex analysis since it preserves many of its key features. After the discovery of the quaternions by William Rowan Hamilton occurred in 1843, the concept of reduced quaternions, referred to quaternions with vanishing third imaginary unit-coefficient, emerged. A modification of quaternionic analysis, based on functions that map from domains of three-dimensional real space ℝ 3 to the set of reduced quaternions, denoted by 𝒜 , has recently been developed. The primary aim of the present paper is to derive an analogue of the Sokhotski–Plemelj formulas for the reduced quaternionic Cauchy-like integral in the context of 𝒜 -valued functions on domains of ℝ 3 with Ahlfors-regular boundary, which is considered distinct from that of quaternionic analysis, despite their natural similarities. Our second task is to establish a Poincaré–Bertrand formula for interchanging the order of integration of two repeated singular reduced quaternionic Cauchy-like integrals, drawing on arguments involving quaternionic analysis. Finally, a Geza Freud-type theorem is proved, as well as some local properties of the singular reduced quaternionic Cauchy-like integral.
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On equivariant embeddings of G-bundles

June 25, 2026

Malkhaz Bakuradze, Ralf Meyer

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For a compact group G , we give a sufficient condition for embedding one G -equivariant vector bundle into another and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of irreducible representations of stabiliser groups. We also apply our results to ordinary nonequivariant vector bundles over the (skew)fields of quaternions, real and complex numbers, as well as to “real” and “quaternionic” vector bundles. Our results apply to the classification of symmetry-protected topological phases of matter, providing computable bounds on the number of energy bands required to distinguish robust from fragile topological phases.
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Explicit formulas for some product series in the white noise theory and Lévy noise analysis

June 25, 2026

Hari M. Srivastava, Aleksandar Petojević

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The main object of this article is to provide closed-form expressions for each of the following sums: 𝒦 q := ∑ α ∈ 𝒥 ( 2 ⁢ ℕ ) - q ⁢ α and 𝒦 ¯ q := ∑ α ∈ 𝒥 ( 2 ⁢ ℕ + 1 ) - q ⁢ α , see text which appear in the analysis of stochastic partial differential equations. Our main results express these sums as finite products of Gamma functions: 𝒦 q = ∏ j = 0 q - 1 Γ ⁢ ( 1 - ω j 2 ) and 𝒦 ¯ q = 2 q π q 2 ⁢ ∏ j = 1 q - 1 Γ ⁢ ( 3 2 - ω j 2 ) , see text where ω = e 2 ⁢ π ⁢ i q is a primitive q th root of unity and q ≧ 2 is a natural number. The relevance and potential uses of explicit evaluations of such product series in, for example, white noise theory and Lévy noise analysis are also indicated.
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On a combinatorial identity of Akyuz and Halici

June 25, 2026

Horst Alzer, Arjun K. Rathie

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Inspired by a combinatorial identity given by Akyuz and Halici, we present three closely related summation formulas. One of our results states that ∑ ν = 0 [ n 2 ] - j ( ν + j m ) ⁢ ( ν + j - m ν ) ⁢ ( n 2 ⁢ ( ν + j ) ) = 2 n - 2 ⁢ j - 1 ⁢ n n - j ⁢ ( n - j j ) ⁢ ( j m ) , see text where m ≥ 0 , j ≥ 0 and n ≥ 1 are integers with m ≤ j ≤ [ n 2 ] . We use properties of hypergeometric functions and the method “comparison of coefficients” to prove our theorems.
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On a periodic problem for second-order Duffing-type equations

June 25, 2026

Alexander Lomtatidze, Jiří Šremr

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The paper addresses the periodic problem u ′′ = p ⁢ ( t ) ⁢ u - q ⁢ ( t , u ) ⁢ u , u ⁢ ( 0 ) = u ⁢ ( ω ) , u ′ ⁢ ( 0 ) = u ′ ⁢ ( ω ) , see text where p : [ 0 , ω ] → ℝ is a Lebesgue integrable function and q : [ 0 , ω ] × ℝ → ℝ is a function satisfying Carathéodory conditions. By combining the maximum and antimaximum principles with the method of non-ordered lower and upper functions, sufficient and necessary conditions are found for the existence of a positive solution to the given problem. The main results are applied and further refined for the equation u ′′ = p ⁢ ( t ) ⁢ u - h ⁢ ( t ) ⁢ φ ⁢ ( u ) ⁢ u , see text whose non-linearity has separated arguments.
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Poincaré’s inequality for the Luxemburg norm of a variable exponent which depends on the test functions

June 25, 2026

Andrei Grecu, Mihai Mihăilescu, Anisia Teca

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In this paper we prove a Poincaré-type inequality within the framework of Luxemburg norms constructed by using some continuous and bounded functions which depend on the test functions.
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Characterization of principal shift-invariant spaces on Vilenkin group

June 25, 2026

Prasadini Mahapatra, Ram Mohapatra

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Translation generated spaces of square-integrable functions on the Vilenkin group are studied using a C-bracket. Principal shift-invariant spaces are characterized via the periodization function and the C-bracket. Conditions for semi-orthogonal Parseval wavelets are established, leading to a generalized multiresolution analysis (GMRA) of the semi-orthogonal Parseval frame. Examples are provided to support and illustrate the theoretical results.
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On periodic problems for non-autonomous Duffing equations and the equation arising from an energy harvester model

June 25, 2026

Alexander Lomtatidze, Jiří Šremr

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We study a periodic problem for the non-autonomous Duffing equation u ′′ = p ( t ) u - h ( t ) | u | λ sgn u ( λ > 1 ) see text and unforced undamped periodic motions of the mechanical part of the energy harvester described by the equation m ⁢ y ′′ + b ⁢ y ′ + k ⁢ y + F mag ⁢ ( t , y ) = f ⁢ ( t ) . see text
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Abstract Korovkin-type theorems via nonlinear operators in modular function spaces with power series methods

June 25, 2026

Sevda Yıldız

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In this paper, we present new abstract versions of Korovkin-type approximation theorems in the framework of modular spaces by employing sequences of monotone and sublinear operators with respect to power series methods. We further calculate the rate of convergence in terms of modulus of continuity and demonstrate the applicability of our abstract results through Bernstein–Kantorovich and Bernstein–Kantorovich–Choquet operators in Orlicz spaces under non-additive measures. Finally, we relax the monotonicity of the sublinear operators in the modular Korovkin theorem.
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Degenerate algorithms for degenerate Bernoulli and Euler numbers

June 25, 2026

Taekyun Kim, Dae San Kim

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This paper introduces and investigates degenerate versions of the A-algorithm and B-algorithm by incorporating a parameter λ into their respective recurrence relations. We derive explicit formulas for the final sequences of these algorithms in terms of the initial sequences and the degenerate Stirling numbers of the second kind. Furthermore, we establish functional relationships between the ordinary generating functions of the initial sequences and the exponential generating functions of the final sequences. Specifically, we demonstrate that these degenerate algorithms yield degenerate Bernoulli and Euler numbers under specific initial conditions.
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G _𝔫-methods and G _𝔫-compactness via nets

June 25, 2026

Osman Mucuk

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Sequences, or more generally, nets, are important in numerous branches of mathematics, such as analysis, number theory and topology. For the reasons explained in introduction, in some works we move from sequences to nets. Considering limits of sequences in a Hausdorff space X assigns a function lim from the set c ⁢ ( X ) of convergent sequences to X . Inspired by this, a G - method , as a generalization of the function lim , is defined by replacing the set c ⁢ ( X ) with a certain class of sequences. Originated by such G -methods, the sequential versions of some fundamental properties in topology, such as continuity, compactness, and connectedness, have been recently generalized by G -methods defined for sequences in sets. This paper presents a study of convergent G 𝔫 -methods involving nets rather than sequences as generalizations of G -methods; and then gives some properties and characterizations of G 𝔫 -compactness and G 𝔫 -countably compactness.
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Characterization of parabolic H ¹ Sobolev spaces by square functions

June 25, 2026

Shuichi Sato

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We consider H 1 -Sobolev spaces associated with the Calderón–Torchinsky Hardy spaces H 1 and characterize these spaces by means of certain square functions. This characterization generalizes and, in fact, improves upon previously known results in the Euclidean setting.
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A new collection of n-tuple operator inequalities

May 28, 2026

Zameddin I. Ismailov, Pembe Ipek Al, Hamid Reza Moradi, Mohammad Sababheh

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In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds constitute a new collection that enriches our understanding of these bounds. We compare our bounds with the existing literature using examples that demonstrate, in general, how our results are incomparable with the known bounds. Of particular interest are the treatment of the triangle inequality, the numerical radius of operator matrices, and singular value bounds for sums of operators.
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Uniform polynomial stability of evolution families via function spaces

May 28, 2026

Pham Viet Hai

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In this paper, we characterize the uniform polynomial stability of evolution families by means of Banach spaces of sequences or functions. This approach provides a framework that not only unifies existing versions of Barbashin-type theorems, but also provides new characterizations.
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Fredholm criteria for the algebra generated by Wiener–Hopf operators with continuous symbols

May 28, 2026

Márcio Valente

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Let X ⁢ ( ℝ + ) be a Lorentz space L p , q ⁢ ( ℝ + ) with 1 < p , q < ∞ or a reflexive Orlicz space L Φ ⁢ ( ℝ + ) . We establish a Fredholm criterion for operators from the Banach algebra generated by all Wiener–Hopf operators with continuous symbols on the space X ⁢ ( ℝ + ) .
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Skew generalized power series rings with the McCoy property

May 28, 2026

Peter Danchev, Masoome Zahiri, Saeide Zahiri

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Let R be a ring, ( S , ⪯ ) a strictly totally ordered monoid and suppose also ω : S → End ⁢ ( R ) is a monoid homomorphism. A skew generalized power series ring R ⁢ [ [ S , ω , ⪯ ] ] consists of all functions from a monoid S to a coefficient ring R whose support contains neither infinite descending chains nor infinite anti-chains, equipped with point-wise addition and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R . Special cases of the skew generalized power series ring construction are the skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Malcev–Neumann series rings and generalized power series rings as well as the untwisted versions of all of these objects. In the present article, we study the so-called ( S , ω ) -McCoy condition on R that is a generalization of the standard McCoy condition from polynomials to skew generalized power series, thereby generalizing some of the existing results in the literature relevant to the subject.
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A study of 2-Toeplitz operator on Köthe spaces

May 28, 2026

Bhawna Gupta, Sparsh Sparsh

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This paper presents the concept of the 2-Toeplitz operator on Köthe spaces, which is a subclass of Fréchet spaces that has recently gained significant prominence in the study of functional analysis and operator theory. We establish detailed characterizations of the continuity and compactness of this operator, providing both necessary and sufficient conditions. Additionally, several concrete examples are provided to illustrate the theoretical results.
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Connections between polynomial sets: A group-theoretic framework

May 28, 2026

Mongi Blel

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This paper develops a comprehensive group-theoretic framework for analyzing transformations and connections between polynomial sets. Building upon the fundamental characterization [Y. Ben Cheikh, Some structures on the polynomial sets, Dolomites Res. Notes Approx., to appear] of the space ℙ of all polynomial sets as the Cartesian product ℙ ≅ Λ ( - 1 ) / ℛ × 𝒮 1 × 𝒮 0 , we introduce and systematically study T -operators acting on this space. These operators provide a unified mechanism for connecting arbitrary polynomial sequences, while stabilizer analysis reveals the inherent symmetry properties of classical polynomial families. Our approach yields powerful new tools for addressing fundamental problems in polynomial theory, including connection coefficients, transformation classification, and the systematic study of relationships between diverse polynomial families. The framework provides both theoretical insights and practical computational methods for working with polynomial sets and their interconnections.
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Normalized solutions for double critical Schrödinger–Poisson system on the first Heisenberg group

May 28, 2026

Xuechun Zheng, Lifeng Guo, Sihua Liang

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This paper investigates the existence and multiplicity of normalized solutions of the double critical Schrödinger–Poisson system on the first Heisenberg group. Together with the truncation techniques, concentration-compactness principle, and genus theory, we establish the existence and multiplicity of normalized solutions for this system. To some extent, the results presented in this paper can be regarded as a supplement and enrichment of previous studies.
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Variable CBMO estimates for commutators of singular integrals with rough kernels

May 28, 2026

Hongbin Wang, Yueyue Yuan

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In this paper, the authors establish variable CBMO estimates for the commutators of singular integrals with rough kernels on variable Herz-type spaces, which extend some known results.
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A note on Spanne-type result on grand Morrey spaces

May 11, 2026

Humberto Rafeiro

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We prove a Spanne-type result for the fractional integral operator on grand Morrey spaces, where the target space is a double-aggrandized Morrey space, while the source space is just a grand Morrey space. This contrasts with the Adams-type result, where both the source and target spaces belong to the same grand Morrey-type space, albeit with different summability parameters.
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On testing hypothesis of equality of two Poisson regression functions

May 11, 2026

Petre Babilua, Elizbar Nadaraya

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The limiting distribution of the integral square deviation between two nonparametric estimators of Poisson regression functions is established. Based on this result, a test for the hypothesis of equality of two Poisson regression functions is constructed. The consistency of the proposed test is also studied.
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Area integrals associated to self-adjoint operators on vector-valued generalized weighted Morrey spaces

May 11, 2026

Chunmei Zhang, Zhidan Wang

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In this paper, we mainly investigate the vector-valued analogs of area integrals associated with self-adjoint operators satisfying Gaussian upper bounds, S P ⁢ f ⁢ ( x ) = ( ∫ 0 ∞ ∫ B ⁢ ( x , t ) | t ⁢ L ⁢ e - t ⁢ L ⁢ f ⁢ ( y ) | 2 ⁢ d ⁢ y ⁢ d ⁢ t t n + 1 ) 1 2 , see text S H ⁢ f ⁢ ( x ) = ( ∫ 0 ∞ ∫ B ⁢ ( x , t ) | t 2 ⁢ L ⁢ e - t 2 ⁢ L ⁢ f ⁢ ( y ) | 2 ⁢ d ⁢ y ⁢ d ⁢ t t n + 1 ) 1 2 . see text The strong-type and weak-type estimates for vector-valued S P and S H in the vector-valued generalized weighted Morrey spaces M w p , φ ⁢ ( ℝ n , l 2 ) are established. Moreover, we obtain the strong estimates of their multilinear commutators S P , b → and S H , b → in the vector-valued generalized weighted Morrey spaces M w p , φ ⁢ ( ℝ n , l 2 ) for 1 < p < ∞ . The boundedness criteria are entirely given via Zygmund-type integral conditions on φ ⁢ ( x , r ) , with no monotonicity requirement for the r -variable.
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Multiple solutions for a nonlinear p(x)-curl system with nonlocal terms via a three critical points theorem

May 11, 2026

Khaled Kefi, Haikel Ouerghi, Khaled Benali

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This paper addresses the existence of multiple weak solutions for a nonlinear curl-type system involving variable exponent growth and nonlocal source terms. We study the p ⁢ ( x ) -curl problem posed in a bounded, simply connected domain 𝔻 ⊂ ℝ 3 , subject to divergence-free and mixed boundary conditions. The system features spatially variable nonlinearities and two integral-type nonlocal terms governed by Carathéodory functions with subcritical growth. Utilizing the framework of variable exponent Sobolev spaces and a three critical points theorem established by Bonanno and Morano, we prove the existence of at least three weak solutions under suitable structural assumptions. This work extends recent developments on variable exponent curl systems and offers new insights into the mathematical modeling of complex physical phenomena exhibiting spatial heterogeneity and nonlocal interactions.
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On the additivity of n-multiplicative isomorphisms, derivations, and related maps in axial algebras

March 26, 2026

Daniel Eiti Nishida Kawai, Henrique Guzzo Jr, Bruno Leonardo Macedo Ferreira

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In this paper, we demonstrate that several classes of functions, specifically n -multiplicative isomorphisms, derivations, elementary maps, and Jordan elementary maps on a class of algebras that includes Jordan algebras with idempotents, 𝒥 ⁢ ( α ) -axial algebras and ℳ ⁢ ( α , β ) -axial algebras, are additive under appropriate conditions, which may be referred to as Martindale-type conditions. Furthermore, we answer the question left open in the recent article [B. L. M. Ferreira, D. A. Smigly and E. Barreiro, Multiplicative isomorphisms and derivations on axial algebras, J. Pure Appl. Algebra 228 (2024), no. 12, Paper No. 107753].

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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

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 Scienc e
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, ItalyEmail: fabio.zanolin@dimi.uniud.it

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eISSN:

1572-9176

ISSN:

1072-947X

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English

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De Gruyter

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First published:

February 1, 1994

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6 issues per year

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eISSN: 1572-9176

ISSN: 1072-947X

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