Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2012; 49(4): 851-861

Printed July 1, 2012

https://doi.org/10.4134/BKMS.2012.49.4.851

Copyright © The Korean Mathematical Society.

Statistical $A$-summability of double sequences and a Korovkin type approximation theorem

Cemal Belen, Mohammad Mursaleen, and Mustafa Yildirim

Cumhuriyet University, Aligarh Muslim University, Cumhuriyet University

Abstract

In this paper, we define the notion of statistical $A$-summability for doublesequences and find its relation with $A$-statistical convergence. We apply our new method of summability to prove a Korovkin-type approximation theorem for a function of two variables. Furthermore, through an example, it is shown that our theorem is stronger than classical and statistical cases.

Keywords: statistical convergence, statistical $A$-summability, Korovkin theorem, double sequence, positive linear operators

MSC numbers: 40A35, 41A36

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