Korovkin type approximation theorem in $A^{Cal I}_{2}$-statistical sense

摘要

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