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.

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

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.,

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.

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

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