Statistical $A$-summability of double sequences and a Korovkin type approximation theorem
Bull. Korean Math. Soc. 2012 Vol. 49, No. 4, 851-861
https://doi.org/10.4134/BKMS.2012.49.4.851
Published online July 1, 2012
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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