Statistical Deferred Euler Summability Mean and Associated Korovokin-type Approximation Theorem

Abstract

Statistical convergence has recently attracted the wide-spread attention of researchers due mainly to the fact that it is more general than the classical convergence. As far as the recent research on the theory and applications of summability is concerned, two basic concepts, namely statistical convergence and Korovokin-type approximation theorems play a very vital role. In the present paper, we introduce the notions of deferred Euler statistical convergence as well as statistical deferred Euler summability means and establish some inclusion relations between them. Furthermore, we prove a Korovokin-type approximation theorem based on our proposed mean, and we also show that our theorem is stronger than the classical versions of Korovokin-type approximation theorem.