The quantum groups nowadays attract a considerable interest of mathematicians and physicists. The theory of 𝑞-special functions has received a group-theoretic interpretation using the techniques of quantum groups and quantum algebras. This paper focuses on introducing the 𝑞-Tricomi functions and 2D 𝑞-Tricomi functions through the generating function and series expansion and for the first time establishing

In this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in

The purpose of the present research is to investigate a general mixed type boundary value problem for the Laplace–Beltrami equation on a surface with the Lipschitz boundary 𝒞 in the non-classical setting when solutions are sought in the Bessel potential spaces Hps⁢(C), 1p

Journal Name: Georgian Mathematical Journal Volume: 27 Issue: 3 Pages: i-iv

Let (ℌ,μ,α) be a regular Hom-algebra of arbitrary dimension and over an arbitrary base field 𝔽. A basis ℬ={ei}i∈I of ℌ is called multiplicative if for any i,j∈I, we have that μ⁢(ei,ej)∈𝔽⁢ek and α⁢(ei)∈𝔽⁢ep for some k,p∈I. We show that if ℌ admits a multiplicative basis, then it decomposes as the direct sum ℌ=⊕rℑr of well-described ideals admitting each one a multiplicative basis. Also, the minimality

Let ℛ be a prime ring, 𝒬r the right Martindale quotient ring of ℛ and 𝒞 the extended centroid of ℛ. In this paper, we discuss the relationship between the structure of prime rings and the behavior of skew derivations on multilinear polynomials. More precisely, we investigate the m-potent commutators of skew derivations involving multilinear polynomials, i.e.,

A new scale of weighted grand mixed norm Lebesgue spaces Lw1p1,φ1⁢(Lw2p2,φ2) is introduced and the boundedness criteria for multiple singular operators are established.

This paper relates to a recent trend in complex differential equations which studies solutions in a given domain. The classical settings in complex equations were widely studied for meromorphic solutions in the complex plane. For functions in the complex plane, we have a lot of results of general nature, in particular, the classical value distributions theory describing numbers of a-points. Many of

The subject of the paper is suggested by G. Janelidze and motivated by his earlier result giving a positive answer to the question posed by S. MacLane whether the Galois theory of homogeneous linear ordinary differential equations over a differential field (which is Kolchin–Ritt theory and an algebraic version of Picard–Vessiot theory) can be obtained as a particular case of G. Janelidze’s Galois theory

We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation

We study the capability property of Leibniz algebras via the non-abelian exterior product.

The support of a wavelet transform associated with a square integrable irreducible representation of a homogeneous space is shown to have infinite measure. Assumptions are illustrated and supported by examples. The pointwise homogeneous approximation property for a wavelet transform has been investigated. An analogue of Heisenberg type inequality is also obtained for a wavelet transform on a wavelet

The paper deals with the exploration of those subclasses of the variable exponent Lebesgue space Lp⁢(⋅) with min⁡p⁢(⋅)=1, which are invariant with respect to Cauchy singular integral operators.

Let ℜ be a ring with center Z⁢(ℜ). In this paper, we study the higher-order commutators with power central values on rings and algebras involving generalized derivations. Motivated by [A. Alahmadi, S. Ali, A. N. Khan and M. Salahuddin Khan, A characterization of generalized derivations on prime rings, Comm. Algebra 44 2016, 8, 3201–3210], we characterize generalized derivations and related maps that

In this paper, we consider a natural extension in the context of d-orthogonality for asymptotic analysis of orthogonal polynomials. We introduce, for several d-orthogonal polynomials, asymptotic expansions in terms of d-Hermite ones. From these expansions, several limits between d-orthogonal polynomials are obtained.

In this paper, we investigate the absolute convergence of Fourier series of functions in several variables for an odd-dimensional space when these functions have continuous partial derivatives. It should be noted that similar properties for an even-dimensional space were given in [L. D. Gogoladze and V. S. Tsagareishvili, On absolute convergence of multiple Fourier series (in Russian), Izv. Vyssh.

The aim of this paper is to introduce generalized Suzuki type F-contraction fuzzy mappings and to prove the existence of fixed fuzzy points for such mappings in the setup of complete ordered metric spaces. An example is provided to show the validity of our results, followed by couple of remarks about the comparison of obtained results with the existing results in the literature. An application of our

We present the conditions for a block matrix of a ring to have the image-kernel (p,q)-inverse in the generalized Banachiewicz–Schur form. We give representations for the image-kernel inverses of the sum and the product of two block matrices. Some characterizations of the image-kernel (p,q)-inverse in a ring with involution are investigated too.

In this paper, we consider a new class of convex functions, called relative h-preivex functions. Seven new inequalities of Hermite–Hadamard type for relative h-preinvex functions are established using different approaches.

The weighted boundedness properties of multilinear operators associated to singular integral operators with non-smooth kernels for extreme cases are obtained.

It is shown that any function acting from the real line ℝ into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function x→exp⁡(x2) cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs

The aim of this paper is to study a quasistatic frictional contact problem for viscoelastic materials with long-term memory. The contact boundary conditions are governed by Tresca’s law, involving a slip dependent coefficient of friction. We focus our attention on the weak solvability of the problem within the framework of variational inequalities. The existence of a solution is obtained under a smallness

In this work, we investigate the spectrum denoted by Λ for the p⁢(x)-biharmonic operator involving the Hardy term. We prove the existence of at least one non-decreasing sequence of positive eigenvalues of this problem such that sup⁡Λ=+∞. Moreover, we prove that inf⁡Λ>0 if and only if the domain Ω satisfies the p⁢(x)-Hardy inequality.

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [H. M. Srivastava, A. Çetinkaya and I. Onur Kıymaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appl. Math. Comput. 226 2014, 484–491] by means of the generalized Pochhammer symbol, we introduce here a new extension of the generalized Mittag-Leffler function

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of sequences of real numbers. Strongly ideal lacunary ward continuity is also investigated. Interesting results are obtained.

In this work, we give a unification and generalization of Laguerre and Hermite polynomials for which the orthogonal property is replaced by d-orthogonality. We state some properties of these new polynomials.

The paper establishes the basic oscillational properties of differential equations of fractional order. It is also shown that the so-called fractional oscillational equation does not have the basic oscillational properties.

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation

Journal Name: Georgian Mathematical Journal Volume: 27 Issue: 2 Pages: i-iv

Four Ulam type stability concepts for non-instantaneous impulsive fractional differential equations with state dependent delay are introduced. Two different approaches to the interpretation of solutions are investigated. We study the case of an unchangeable lower bound of the Caputo fractional derivative and the case of a lower bound coinciding with the point of jump for the solution. In both cases

In this paper, we investigate the strong summability of two-dimensional Walsh–Fourier series obtained in [F. Weisz, Strong convergence theorems for two-parameter Walsh–Fourier and trigonometric-Fourier series, Studia Math. 117 1996, 2, 173–194] (see Theorem ) and prove the sharpness of this result.

For certain families of topologies, the existence of a common Sierpiński–Zygmund function (of a common Sierpiński–Zygmund function in the strong sense) is established. In this connection, the notion of a Sierpiński–Zygmund space (of a Sierpiński–Zygmund space in the strong sense) is introduced and examined. The behavior of such spaces under some standard topological operations is considered.

The purpose of this paper is to provide a cohomology of n-Hom-Leibniz algebras. Moreover, we study some higher operations on cohomology spaces and deformations.

In this paper, we establish weighted higher order exponential type inequalities in the geodesic space (X,d,μ) by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined

In this paper we study the boundedness of localization operators associated with the Stockwell transform with symbol in Lp acting on the Wiener amalgam space W⁢(Lp,Lq)⁢(ℝ).

We prove some trigonometric identities involving Chebyshev polynomials of the second kind. The identities were inspired by atomic form factor calculations. Generalizations of these identities, if found, will help to increase the numerical stability of atomic form factor calculations for highly excited states.

The paper is devoted to the construction and study of the additive averaged semi-discrete scheme for one nonlinear multi-dimensional integro-differential equation of parabolic type. The studied equation is based on the well-known Maxwell’s system arising in mathematical simulation of electromagnetic field penetration into a substance.

Consider the first-order linear differential equation with several non-monotone retarded arguments x′⁢(t)+∑i=1mpi⁢(t)⁢x⁢(τi⁢(t))=0, t≥t0, where the functions pi,τi∈C⁢([t0,∞),ℝ+), for every i=1,2,…,m, τi⁢(t)≤t for t≥t0 and limt→∞⁡τi⁢(t)=∞. New oscillation criteria which essentially improve the known results in the literature are established. An example illustrating the results is given.

The purpose of the present research is to investigate model mixed boundary value problems (BVPs) for the Helmholtz equation in a planar angular domain Ωα⊂ℝ2 of magnitude α. These problems are considered in a non-classical setting when a solution is sought in the Bessel potential spaces ℍps⁢(Ωα), s>1p, 1

We prove that if the transpose of every 2×2 idempotent matrix over a division ring D, different from the identity matrix, is not invertible, then D is commutative.

In the present paper, we discuss the approximation properties of Jain–Baskakov operators with parameter c. The paper deals with the modified forms of the Baskakov basis functions. Some direct results are established, which include the asymptotic formula, error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct the King modification of these operators, which

The predual spaces of generalized grand Morrey spaces over non-doubling measure spaces are investigated. The case of the grand Lebesgue spaces is covered, which is also new. An example shows that the modification of Morrey spaces is essential.

The main goal of this article is to derive differential and associated integral equations for some 2-iterated and mixed type special polynomial families. By using the factorization method, the recurrence relations and differential equations are derived for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials. The Volterra integral equations for these polynomial families are also

Given a matrix A such that AM=I and 0≤α

Internal points were introduced in the literature of topological vector spaces to characterize the finest locally convex vector topology. In this manuscript we generalize the concept of internal point in real vector spaces by introducing a type of points, called inner points, that allows us to provide an intrinsic characterization of linear manifolds, which was not possible by using internal points

An interesting question about the perturbed sequences is: when do they inherit the properties of the original one? An elegant relation between frames (fusion frames) and their perturbations is the relation of their redundancies. In this paper, we investigate these relationships. Also, we express the redundancy of frames (fusion frames) in terms of the cosine angle between some subspaces.

In this study, we extend the concepts and fundamental results on statistical convergence from a single time scale to any product time scale. Various characterizations about these new notions are also obtained.

We extend the quantitative Balian–Low theorem of Nitzan and Olsen to higher dimensions. We use Zak transform methods and dimension reduction. The characterization of the Gabor–Riesz bases by the Zak transform allows us to reduce the problem to the quasiperiodicity and the boundedness from below of the Zak transforms of the Gabor–Riesz basis generators, two properties for which dimension reduction is

The aim of this paper is to study the algebraic aspects of the gluing procedure in the category of differential spaces. In particular, the Sikorski differential spaces are studied. The algebraic techniques are mainly based on the spectral approach. This paper is a continuation of some previous researches in differential spaces techniques.

In the present paper we establish a general form of Voronovskaja’s theorem for functions defined on an unbounded interval and having exponential growth. The case of approximation by linear combinations is also considered. Applications are given for some Szász–Mirakyan and Baskakov-type operators.

Let μ be a nonnegative Borel measure on the unit disk 𝔻. In this paper, we investigate measures μ such that the weighted BMOA spaces are embedded boundedly or compactly into tent-type spaces 𝒯φ∞⁢(μ). As an application, we characterize the boundedness and compactness of Volterra integral operators on the weighted BMOA space.

We introduce and investigate the adjoint resolutions and adjoint dimensions of modules. As a consequence, we give some new characterizations of weak global dimensions of coherent rings in terms of adjoint resolutions and adjoint dimensions of modules.

In this paper, the analysis of an HIV-1 epidemic model is presented by incorporating a distributed intracellular delay. The delay term represents the latent period between the time that the target cells are contacted by the virus and the time the virions penetrated into the cells. To understand the analysis of our proposed model, the Rouths–Hurwiz criterion and general theory of delay differential