Korovkin type approximation theorem in A2I-statistical sense

Abstract

In this paper we consider the notion of $A_{\mathcal{2}}^{\mathcal{I}}$-statistical convergencefor real double sequences which is an extension of the notion of $A^{\mathcal{I}}$-statistical convergencefor real single sequences introduced by Savas, Das and Dutta. We primarily applythis new notion to prove a Korovkin type approximation theorem.In the last section, we study the rate of $A_{\mathcal{2}}^{\mathcal{I}}$-statistical convergence.