Statistical Convergence with Respect to Power Series Methods and Applications to Approximation Theory

Abstract

In this article we introduce the concepts of -statistical convergence and Pp-strong convergence that are introduced via power series methods. Introducing a new type of uniform integrability with the help of power series method we obtain a relationship between these concepts which is actually a characterization of the concept of Pp-strong convergence. As an application we give a Korovkin type approximation theorem by using Pp-statistical convergence and also present an example to illustrate that Pp-statistical approximation is stronger than uniform approximation.