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http://dx.doi.org/10.4134/BKMS.2010.47.4.825

A KOROVKIN TYPE APPROXIMATION THEOREM FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS OF TWO VARIABLES IN A-STATISTICAL SENSE  

Demirci, Kamil (FACULTY OF SCIENCES AND ARTS DEPARTMENT OF MATHEMATICS SINOP UNIVERSITY)
Dirik, Fadime (FACULTY OF SCIENCES AND ARTS DEPARTMENT OF MATHEMATICS SINOP UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.4, 2010 , pp. 825-837 More about this Journal
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.
Keywords
A-statistical convergence for double sequences; positive linear operator; Korovkin type approximation theorem; Meyer-K$\ddot{o}$nig and Zeller operator; modulus of continuity;
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