Four-dimensional matrix transformation and rate of A-statistical convergence of periodic functions
In this paper, using the concept of A-statistical convergence for double real sequences, we obtain a Korovkin type-approximation theorem for double sequences of positive linear operators defined on the space of all 2 pi-periodic and real valued continuous functions on the real two-dimensional space. Furthermore, we display an application which shows that our new result is stronger than its classical version. Also, we study rates of A-statistical convergence of a double sequence of positive linear operators acting on this space. Finally, displaying an example, it is shown that our statistical rates are more efficient than the classical aspects in the approximation theory. (C) 2010 Elsevier Ltd. All rights reserved.
2 pi-periodic and real valued continuous functions the korovkin type-approximation theorem rates of a-statistical convergence for double sequences regularity for double sequences