Korovkin Type Approximation Theorem via $A^\mathcal {I}_2$-Summability Methods

Abstract

In this paper we consider the notion of $A^\mathcal {I}_2$-summability for real double sequences which is an extension of the notion of $A^\mathcal {I}$-summability for real single sequences introduced by Savas et.al. We primarily apply this new notion to prove a Korovkin type approximation theorem. In the last section, we study the rate of $A^\mathcal {I}_2$-summability.