Korovkin-type approximation theorem for Bernstein Stancu operator of rough statistical convergence of triple sequence

Ayten Esi,Nagarajan Subramanian,Mustafa Kemal Ozdemir

doi:10.5269/bspm.v38i7.45874

Ayten Esi, Nagarajan Subramanian + Show 1 more

Open Access

https://doi.org/10.5269/bspm.v38i7.45874

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Abstract

We obtain a Korovkin-type approximation theorem for Bernstein Stancu polynomials of rough statistical convergence of triple sequences of positive linear operators of three variables from $H_{\omega}\left( K\right) $ to $C_{B}\left( K\right) $, where $K=[0,\infty)\times\lbrack0,\infty )\times\lbrack0,\infty)$ and $\omega$ is non-negative increasing function on $K$.

Highlights

Aytar [3] studied of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained two statistical convergence criteria associated with this set and prove that this set is closed and convex
Korovkin approximation theory which deals with the problem of approximation of function f by the sequence (Tm(f, x)) where (Tm) is a sequence of positive linear operators [21], [24]
We prove an analogue of the classical Korovkin theorem by using of ideal lambda summability

Summary

Introduction

Aytar [3] studied of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained two statistical convergence criteria associated with this set and prove that this set is closed and convex. In this paper we investigate some basic properties of Korovkin-type approximation theorem for rough statistical convergence of a triple sequences in six dimensional matrix which are not discussed earlier.

Results

Conclusion