S. A. Mohiuddine

• PhD
• Professor at King Abdulaziz University

This work introduces τ$$ \tau $$‐Bézier–Bernstein‐integral type operators, along with local approximation results, a direct approximation theorem that leverages the Ditzian–Totik modulus of smoothness, and a quantitative Voronovskaja‐type theorem using the Ditzian–Totik modulus of continuity. Additionally, we derive the convergence rate for differe...

We have proposed a $ q $-analogue $ c(\mathcal{F}(q)) $ and $ c_0(\mathcal{F}(q)) $ of Fibonacci sequence spaces, where $\mathcal{F}(q) = (f^q_{km})$ denotes a $ q $-Fibonacci matrix defined in the following manner: \begin{document}$ f^q_{km} = \begin{cases} q^{m+1} \frac{f_{m+1}(q)}{f_{k+3}(q) - 1}, & \text{if } 0 \leq m \leq k, \\ 0, & \text{if }...

In this paper, we attempt to use the Dunkl analog to study the convergence properties of q-Phillips operators by using the q-Appell polynomials. By applying the new sequences of continuous functions νs,q(z)=(z−12[s]q)ϱ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbs...

In this research paper, we construct a new sequence of Riemann–Liouville type fractional α$$ \alpha $$‐Bernstein–Kantorovich operators. We prove a Korovkin type approximation theorem and discuss the rate of convergence with the first order modulus of continuity of these operators. Further, we study Voronovskaja type theorem, quantitative Voronovska...

In the present article we want to study the convergence and other related properties of Schurer type Bernstein–Kantorovich–Stancu operators with Shifted knots. First we design the Bernstein–Kantorovich operators of the of Stancu type polynomials by Shifted knots of real parameters by including the Schurer positive real parameters, then obtain the c...

In this work, we define Orlicz–Euler double sequence space \({\mathscr {E}}^{r,s}_{\varphi }\) and Orlicz–Taylor double sequence space, \({\mathscr {T}}^{r,s}_{\varphi }\) and obtain certain inclusion results related to these spaces. We further focus on estimating the upper bounds for \(\left\| {\mathfrak {T}}\right\| _{{\mathscr {L}}_{\varphi },{\...

We develop new Banach sequence spaces e 0 a , b p , q and e c a , b p , q derived by the domain of generalized p , q -Euler matrix E a , b p , q in the spaces of null and convergent sequences, respectively. We investigate some topological properties and inclusion natures related to these spaces. We construct bases and obtain α , β , and γ -duals of...

In this manuscript, we construct new modification of Baskakov operators on (0,?) using the second central moment of the classical Baskakov operators. And the moments and the central moments computation formulas and their quantitative properties are computed. Then, rate of convergence, point-wise estimates, weighted approximation and Voronovskaya ty...

In this paper, we consider a bivariate extension of blending type approximation by Lupa?-Durrmeyer type operators involving P?lya Distribution. We illustrate the convergence rate of these type operators using Peetre?s K-functional, modulus of smoothness and for functions in a Lipschitz type space.

We introduce the sequence of Stancu variant of α-Schurer-Kantorovich operators and systematically investigate some basic estimates. We also obtain the uniform convergence theorem and the order of approximation in terms of suitable modulus of continuity for our newly defined operators. Moreover, we investigate rate of convergence by means of Peetre'...

We aim to investigate and study vector-valued multiplier spaces with reference to the sequences of continuous linear operators among normed spaces and deferred Nörlund summability. Further, we obtain some characterization of completeness of the spaces with respect to the vector valued null multiplier convergent operator series. Furthermore, we inve...

In this chapter, we introduce q-Euler difference sequence spaces e0q(Δ) and ecq(Δ) derived by composition of the q-Euler matrix and the difference matrix Δ in the spaces c0 and c, respectively. We obtain the Schauder bases, α-, β-, and γ-duals of the new spaces e0q(Δ) and ecq(Δ). We characterize certain classes of matrix mappings from the spaces e0...

In our discussion, existence of solution for fractional integral equation (FIE) involving (k, z)-Riemann–Liouville fractional integral is studied. To achieve this goal, first using shifting distance functions, we establish a new generalization of Dorbo-type fixed point theorem, in short, we shall write DFPT, and then we apply our DFPT on aforementi...

In this article, we introduce the notion of \((\alpha -\beta )\)-level spaces by considering the concept of fuzzy bitopological space (shortly, fbts). We also define the fuzzy bitopological \((\alpha -\beta )\)-Hausdorff space and, with the help of \((\alpha -\beta )^{*}\)-disjoint sets, the idea of fuzzy bitopological \((\alpha -\beta )^{*}\)-Haus...

We construct the Schurer–Kantorovich operators depending on the shape parameter α∈[0,1] which we called α-Schurer–Kantorovich operators, and estimate their moments and central moments. We discuss the uniform convergence as well as the rate of convergence in terms of modulus of smoothness and Lipschitz-type functions, and other related results for o...

In this study, we construct the difference sequence spaces p P∇ 2 q = (p) P∇ 2 q , 1 ≤ p ≤ ∞, where P = (rs) is an infinite matrix of Padovan numbers s defined by rs =        s r+5 −2 0 ≤ s ≤ r, 0 s > r. and ∇ 2 q is a q-difference operator of second order. We obtain some inclusion relations, topological properties, Schauder basis and α-, β-...

In the present manuscript, we consider ?-Bernstein-Durrmeyer operators involving a strictly positive continuous function. Firstly, we prove a Voronovskaja type, quantitative Voronovskaja type and Gr?ss-Voronovskaja type asymptotic formula, the rate of convergence by means of the modulus of continuity and for functions in a Lipschitz type space. Fin...

In this manuscript, we consider the Baskakov-Jain type operators involving two parameters ? and ?. Some approximation results concerning the weighted approximation are discussed. Also, we find a quantitative Voronovskaja type asymptotic theorem and Gr?ss Voronovskaya type approximation theorem for these operators. Some numerical examples to illustr...

The aim of this work is to give some fixed point results based on the technique of measure of noncompactness which extend the classical Darbo’s theorem. With the help of our Darbo-type theorem, we obtain the existence of solution of implicit fractional integral equations in C(I,ℓpα) (collection of all continuous functions from I=[0,a] (a>0) to ℓpα)...

In the present work, we construct a new sequence of positive linear operatorsinvolving Pólya distribution. We compute a Voronovskaja type and a Grüss–Voronovskaja type asymptotic formula as well as the rate of approximation by using the modulus of smoothness and for functions in a Lipschitz type space. Lastly, we provide some numerical results, whi...

In this work, we define some difference sequence spaces based upon Lucas band matrix and associated with the idea of sequence of modulus functions and then establish that aforementioned spaces are BK-spaces of non absolute type.We further investigate that our spaces are linearly isomorphic to the space l(p), where \(l(p)=\{x=(x_{k}) \in w:\sum _{k}...

In this work, we construct the genuine Durrmeyer–Stancu type operators depending on parameter α in [0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[0,1]$\end{docume...

We construct the Baskakov–Kantorovich operators based on shape parameter \(\alpha\) by linking with Stancu operators to approximate functions over unbounded intervals. We establish local approximation results with the help of suitable modulus of continuity, \({\mathcal {K}}\)-functional and Lipschitz-type space. Further, we obtain the weighted appr...

In the present paper, we introduce and study ideal convergence of some fuzzy sequence spaces via lacunary sequence, infinite matrix and Orlicz function. We study some topological and algebraic properties of these spaces. We also make an effort to show that these spaces are normal as well as monotone. Further, it is very interesting to show that if...

We construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K-functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the...

In this article we introduce the generalized Fibonacci difference operator F(B) by the composition of a Fibonacci band matrix F and a triple band matrix B(x,y,z) and study the spaces ℓk(F(B)) and ℓ∞(F(B)). We exhibit certain topological properties, construct a Schauder basis and determine the Köthe–Toeplitz duals of the new spaces. Furthermore, we...

In the present paper, we intend to make an approach to introduce and study the applications of fractional-order difference operators by generating Orlicz almost null and almost convergent sequence spaces. We also show that aforesaid spaces are linearly isomorphic and BK-spaces. Further, we investigate inclusion relations between newly formed sequen...

In this work, we construct a Durrmeyer type modification of the τ-Baskakov operators depends on two parameters α>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha...

In this work, we construct a new kind of Bernstein-Schurer operators which includes non-negative real parameter α. We study some shape preserving properties, namely, monotonicity and convexity of the new operators. We obtain global approximation formula in terms of Ditzian-Totik uniform modulus of smoothness of first and second order and calculate...

In this paper, we introduce Padovan difference sequence spaces of fractional-order [Formula: see text] [Formula: see text] [Formula: see text] by the composition of the fractional-order difference operator [Formula: see text] and the Padovan matrix [Formula: see text] defined by [Formula: see text] and [Formula: see text] respectively, where the se...

Using the notion of forward and backward arithmetic convergence in asymmetric metric space, we define arithmetic $ff$-continuity and arithmetic $fb$-continuity and prove some interesting results in asymmetric metric space. Finally, we introduce the concept of forward (or backward) arithmetic compactness and give some interesting results in asymmetr...

The aim of this paper is to define two sorts of convergence in measure, that is, outer and inner statistical convergence, for double sequences of fuzzy-valued measurable functions and demonstrate that both kinds of convergence are equivalent in a finite measurable set. We also define the notion of statistical convergence in measure for double seque...

We construct the Stancu variant of Bernstein–Kantorovich operators based on shape parameter α. We investigate the rate of convergence of these operators by means of suitable modulus of continuity to any continuous functions f(x) on (x\in [0,1]) and Voronovskaja-type approximation theorem. Moreover, we study other approximation properties of our new...

In this article, we introduce binomial weighted sequence spaces \(b_p^{r,s}(w)\)\((1\le p<\infty )\), where \(w=(w_n)\) is a non-negative decreasing sequence of real numbers, and investigate some topological and inclusion properties of the new spaces. We give an upper estimation of \(\left\| A\right\| _{\ell _p(w),b_p^{r,s}(w)}\), where A is the Ha...

In the proposed paper, we have introduced the notion of point-wise relatively statistical convergence, relatively equi-statistical convergence and relatively uniform statistical convergence of sequences of functions based on the difference operator of fractional order including (p, q)-gamma function via the deferred Nörlund mean. As an application...

In this paper, we introduce some generalized entire sequence spaces and analytic sequence spaces defined by fractional difference operator and a sequence of modulus functions. We study some topological properties and give some inclusion relations among the spaces.

The aim of this article is to establish the existence of the solution of non-linear functional integral equations x(l,h)=U(l,h,x(l,h))+Fl,h,∫0l∫0hP(l,h,r,u,x(r,u))drdu,x(l,h)×Gl,h,∫0a∫0aQl,h,r,u,x(r,u)drdu,x(l,h) of two variables, which is of the form of two operators in the setting of Banach algebra C[0,a]×[0,a],a>0. Our methodology relies upon th...

The purpose of this paper is to introduce the new concept of weighted statistical convergence and strong weighted summability of order β for sequences of fuzzy numbers involving the ideas of difference operators and two sequences p=(pn), q=(qn) of positive numbers, and establish the relationship between these notions. Finally, as an application, we...

This paper is devoted to studying weighted A-statistical convergence and statistical weighted A-summability of fuzzy sequences and their representations of sequences of λ-levels, which are intervals. We obtain necessary and sufficient conditions for the matrix A to be weighted fuzzy regular and derive some inclusion relations concerning these newly...

We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter λ∈[−1,1] and calculate their moments. The uniform convergence of the operator and global approximation result by means of Ditzian-Totik modulus of smoothness are established. Also, we establish the direct approximation theorem with the help of second order modul...

© 2018 Advances in Summability and Approximation Theory Editors: Mohiuddine, S. A., Acar, Tuncer (Eds.) Discusses the theory of classical and modern methods in summability Includes a technique for studying the existence of solutions of infinite systems of differential equations in Banach sequence spaces Introduces the approximation of functions by...

We introduce the notion of ideally relative uniform convergence of sequences of real valued functions. We then apply this notion to prove Korovkin-type approximation theorem, and then construct an illustrative example by taking (p,q)-Bernstein operators which proves that our Korovkin theorem is stronger than its classical version as well as statist...

The “oldest quartic” functional equation f(x+2y)+f(x-2y)=4[f(x+y)+f(x-y)]-6f(x)+24f(y) was introduced and solved by the second author of this paper (see J. M. Rassias, Solution of the Ulam stability problem for quartic mappings, Glas. Mat. Ser. III 34(54) 1999, 2, 243–252). Similarly, an interesting “quintic” functional equation was introduced and...

We introduce the notions of weighted lacunary statistical pointwise and uniform convergence and a kind of convergence which is lying between aforementioned convergence methods, namely, weighted lacunary equi-statistical convergence and obtain various implication results with supporting examples. We then apply our new concept of weighted lacunary eq...

The present paper deals with the Stancu-type generalization of (p, q)-Baskakov-Durrmeyer operators. We investigate local approximation, weighted approximation properties of new operators and present the rate of convergence by means of suitable modulus of continuity. At the end of the paper, we introduce a new modification of (p, q)-Baskakov-Durrmey...

The present paper deals with genuine Bernstein–Durrmeyer operators which preserve some certain functions. The rate of convergence of new operators via a Peetre \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\...

We first define the notion of lacunary statistical convergence of order (α,β) , and taking this notion into consideration, we introduce some seminormed difference sequence spaces over n -normed spaces with the help of Musielak-Orlicz function M=(Mk) of order (α,β) . We also examine some topological properties and prove inclusion relations between t...

The aim of this paper is to obtain existence results for an infinite system of differential equations of order n with boundary conditions in the Banach spaces c0 and ℓ1 with the help of a technique associated with measures of noncompactness. We also provide some illustrative examples in support of our existence theorems.

We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in \(g(\mathcal{M},\Delta^{(m)}, v, p)\). We also make an effort to...

In the present paper we introduce and study some generalized difference sequence spaces of invariant means defined by ideal and a sequence of modulus functions over n-normed space. We study some topological properties and prove some inclusion results between these spaces. Further, we also study some results on statistical convergence. © 2018 Forum-...

This paper is devoted to extend the notion of almost convergence and its statistical forms with respect to the difference operator involving (p, q)-gamma function and an increasing sequence \((\lambda _n)\) of positive numbers. We firstly introduce some new concepts of almost \({\Delta }^{[a,b,c]}_{h, \alpha , \beta }(\lambda )\)-statistical conver...

The purpose of this paper is to introduce the notion of weighted almost convergence of a sequence and prove that this sequence endowed with the sup-norm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddside...

In the present paper, we introduce Stancu type generalization of (p; q)-Szasz-Mirakyan-Baskakov operators and investigate their approximation properties such as weighted approximation, rate of convergence and pointwise convergence.

The present paper deals with the construction of Baskakov Durrmeyer operators, which preserve the linear functions, in (p,q) -calculus. More precisely, using (p,q) -Gamma function we introduce genuine mixed type Baskakov Durrmeyer operators having Baskakov and Szász basis functions. After construction of the operators and calculations of their mome...

In the present paper, we construct a new sequence of Bernstein Kantorovich operators depending on a parameter α. The uniform convergence of the operators, rate of convergence in local and global senses in terms of first and second order modulus of continuity are studied. Some graphs and numerical results presenting the advantages of our constructio...

The purpose of this paper is to introduce some new sequence spaces of fuzzy numbers defined by lacunary ideal convergence using generalized difference matrix and Orlicz functions. We also study some algebraic and topological properties of these classes of sequences. Moreover, some illustrative examples are given in support of our results.

We define the notions of pointwise and uniform statistical convergence of double sequences of fuzzy valued functions and obtain relationships between these two kinds of convergence. We further introduce the notion of equi-statistical convergence of double sequences of fuzzy valued functions and show that uniformly statistically convergent double se...

We introduce (θ,m)-uniform lacunary density of any set and (θ,m)-uniform lacunary statistical convergence on an arbitrary time scale. Moreover, (θ,m)-uniform strongly p-lacunary summability and some inclusion relations about these new concepts are also presented

In the present paper, we introduce Kantotovich modifications of (p, q)-Bernstein operators using a new (p, q)-integral. We first estimate the moments and central moments. We obtain uniform convergence of new operators, rate of convergence in terms of classcical modulus of continuity and second order modulus of continuity. We also investigate the ra...

We introduce some fuzzy set-valued functional equations, i.e. the generalized Cauchy type (in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic-Jensen type fuzzy set-valued functional equations and discuss the Hyers-Ulam-Rassias stability of the above said functional equations. These results can be regarded a...

The aim of paper is to define and study some ideal convergent sequence spaces with the help of generalized difference matrix Bⁿ(m) and Orlicz functions. We also make an effort to study some algebraic and topological properties of these difference sequence spaces.

In this article, we use the technique based upon measures of noncompactness in conjunction with a Darbo-type fixed point theorem with a view to studying the existence of solutions of infinite systems of second-order differential equations in the Banach sequence space ℓp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepack...

In this paper, we derive some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence space \(\ell_{p}(r,s,t;B^{(m)})\) which is related to \(\ell_{p}\) spaces. By applying the Hausdorff measure of noncompactness, we obtain the necessary and sufficient conditions for su...

In this paper, we are introducing pertinent Euler–Lagrange–Jensen type k-quintic functional equations and investigate the ‘Ulam stability’ of these new k-quintic functional mappings f:XY, where X is a real normed linear space and Y a real complete normed linear space. We also solve the Ulam stability problem for Euler–Lagrange–Jensen alternative k-...

In the present paper, we introduce Kantotovich modifications of (p, q)-Bernstein operators for bivariate functions using a new (p, q)-integral. We first estimate the moments and central moments. We give the uniform convergence of new operators, rate of convergence in terms of modulus of continuity. The approximations behaviours of the operators for...

The “oldest quartic” functional equation was introduced and solved by the author of this paper (see: Glas. Mat. Ser. III 34 (54) (1999), no. 2, 243-252) which is of the form: f(x + 2y) + f(x − 2y) = 4[f(x + y) + f(x − y)] − 6f(x)+ 24f(y). Interesting results have been achieved by S.A. Mohiuddine et al., since 2009. In this paper, we are introducing...

We introduce the notion of statistical weighted A-summability of a sequence and establish its relation with weighted A-statistical convergence. We also define weighted regular matrix and obtain necessary and sufficient conditions for the matrix A to be weighted regular. As an application, we prove the Korovkin type approximation theorem through sta...

The concern of this paper is to introduce a Kantorovich modification of (p,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$( p,q ) $\end{document}-Baskakov operators a...

In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist". In 1982-2013, the second author solved the above Ulam problem for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2...

Korovkin-type approximation theory usually deals with convergence analysis for sequences of positive operators. This approximation theorem was extended to more general space of sequences via different way such as statistical convergence, summation processes. In this work, we introduce a new type of statistical product summability, that is, statisti...

In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist”. In 1982-2013, the second author solved the above Ulam problem for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2...

In the present paper, we introduce Stancu type generalization of (p, q)-Szasz-Mirakyan-Baskakov operators and investigate their approximation properties such as weighted approximation, rate of convergence and pointwise convergence.

The “oldest cubic” functional equation was introduced and solved by the second author of this paper (see: Glas. Mat. Ser. III 36(56) (2001), no. 1, 63-72). which is of the form: f(x + 2y) = 3f(x + y) + f(x - y) - 3f(x) + 6f(y) For further research in various normed spaces, we are introducing new cubic functional equations, and establish fundamental...

Korovkin-type approximation theory usually deals with convergence analysis for sequences of positive operators. This approximation theorem was extended to more general space of sequences via different way such as statistical convergence, summation processes. In this work, we introduce a new type of statistical product summability, that is, statisti...

Recently, the idea of asymptotic density of order α has been introduced by Bhunia et. al. in [7]. In the present paper we introduce the notion of uniform density of order α and define and study related convergence methods so-called Iu-convergence of order α and uniform strong p-Cesàro convergence of order α. Furthermore, some examples are displayed...

In this paper, we characterize the matrix classes ( ℓ 1 , ℓ p ( F ˆ ) ) ( 1 ≤ p < ∞ ), where ℓ p ( F ˆ ) is some Fibonacci difference sequence spaces. We also obtain estimates for the norms of the bounded linear operators L A defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operato...

In this paper, we prove some tripled fixed point theorems for Meir-Keleer condensing operator in a Banach space by using L-functions. We apply these results to establish the existence of solutions for a system of functional integral equations of Volterra type.

The guest editors of this special issue would like to express their gratitude to the authors who have submitted papers for consideration. The editors thank all the contributors and colleagues who did the refereeing work very sincerely.

The purpose of this paper is to introduce some sequence spaces of fuzzy numbers defined by a Musielak-Orlicz function. We also make an effort to study some topological properties and prove some inclusion relations between these spaces.

We introduce some new generalized difference sequence spaces by means of ideal convergence, infinite matrix, and a sequence of modulus functions over -normed spaces. We also make an effort to study several properties relevant to topological, algebraic, and inclusion relations between these spaces.

The concept of statistical summability (C, 1) has recently been introduced by Moricz (2002). In this paper, we use this notion of summability to prove the Korovkin type approximation theorem for functions of two variables. Finally we construct an example by Bleimann, Butzer and Hahn operators to show that our result is stronger than those of previo...

G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84- 92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo’s fixed point theorem for solving infinite system of linear equations in some sequenc...

The aim of this special issue is to focus on recent developments and achievements in the theory of function spaces, sequences spaces and their geometry, and compact operators and their applications in various fields of applied mathematics, engineering, and other sciences. The theory of sequence spaces is powerful tool for obtaining positive results...

In this paper we define the sequence space V∞σ(λ) related to the concept of invariant mean and de la Vallée-Pousin mean. We also determine the necessary and sufficient conditions to characterize the matrices which transform paranormed sequence spaces into the spaces Vσ(λ) and V∞σ(λ), where Vσ(λ) denotes the space of all (σ, λ)-convergent sequences....

Korovkin type approximation theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them. In this paper, we prove Korovkin type approximation theorems for functions of two variables by using different sets of test functions through cr-convergence of double sequences. We also...

The aim of this special issue is to focus on the latest developments and achievements of the theory of compact operators on function spaces and their applications in differential , functional, and integral equations. The concept of the compactness plays a fundamental role in creating the basis of several investigations conducted in nonlinear analys...

The aim of this paper is to introduce some generalized spaces of double sequences with the help of the Musielak-Orlicz function M=(Mjk) and four-dimensional bounded-regular (shortly, RH-regular) matrices A=(anmjk) over n-normed spaces. Some topological properties and inclusion relations between these spaces are investigated. MSC: 40A05, 40D25.