The generalization of bivariate MKZ operators by multiple generating functions

The notion of statistical weighted -summability was introduced very recently (Kadak et al. in Appl. Math. Comput. 302:80–96, 2017). In the paper, we study the concept of statistical deferred weighted -summability and deferred weighted -statistical convergence and then establish an inclusion relation between them. In particular, based on our proposed methods, we establish a new Korovkin-type approximation theorem for the functions of two variables defined on a Banach space and then present an illustrative example to show that our result is a non-trivial extension of some traditional and statistical versions of Korovkin-type approximation theorems which were demonstrated in the earlier works. Furthermore, we establish another result for the rate of deferred weighted -statistical convergence for the same set of functions via modulus of continuity. Finally, we consider a number of interesting special cases and illustrative examples in support of our findings of this paper.

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“…Now we recall the generating function type Meyer–König and Zeller operators of two variables (see [ 30 ] and [ 31 ]).…”

Section: A Korovkin-type Theorem Via Statistical Deferred Weighted mentioning

confidence: 99%

Statistical deferred weighted B $\mathcal{B}$ -summability and its applications to associated approximation theorems

2018

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“…If we replace the matrix A in Theorem 1 by identity double matrix, then we immediately get the following classical result, which was first introduced by Taşdelen and Erençin [17].…”

Section: Throughout This Section Letmentioning

confidence: 92%

A Korovkin Type Approximation Theorem for Double Sequences of Positive Linear Operators of Two Variables in a-Statistical Sense

Demirci¹,

Dirik²

2010

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we obtain a Korovkin type approximation theorem for double sequences of positive linear operators of two variables from H w (K) to C (K) via A-statistical convergence. Also, we construct an example such that our new approximation result works but its classical case does not work. Furthermore, we study the rates of A-statistical convergence by means of the modulus of continuity.

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“…Recently, there is a growing interest in defining linear positive operators via special functions (see [2][3][4][5][6][7][8][9][10][11][12][13]). In particular, many authors have studied various generalizations of Szasz operators via special functions.…”

Section: Introductionmentioning

confidence: 99%

A Kantorovich-Stancu Type Generalization of Szasz Operators including Brenke Type Polynomials

Aktaş

Çekіm

Taşdelen

2013

Journal of Function Spaces and Applications

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The generalization of bivariate MKZ operators by multiple generating functions

Cited by 12 publications

References 11 publications

Statistical deferred weighted B $\mathcal{B}$ -summability and its applications to associated approximation theorems

Statistical deferred weighted B $\mathcal{B}$ -summability and its applications to associated approximation theorems

A Korovkin Type Approximation Theorem for Double Sequences of Positive Linear Operators of Two Variables in a-Statistical Sense

A Kantorovich-Stancu Type Generalization of Szasz Operators including Brenke Type Polynomials

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