A Korovkin type approximation theorem for double sequences of positive linear operators of two variables in $A$-statistical sense
Bull. Korean Math. Soc. 2010 Vol. 47, No. 4, 825-837
https://doi.org/10.4134/BKMS.2010.47.4.825
Published online July 1, 2010
Kamil Demirci and Fadime Dirik
Sinop University, Sinop University
Abstract : In this paper, we obtain a Korovkin type approximation theorem for double sequences of positive linear operators of two variables from $H_{w}\left( K\right) $ to $C\left( K\right) $ 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\{o}nig and Zeller operator, modulus of continuity
MSC numbers : 41A25, 41A36, 47B38
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