Statistical Convergence with Respect to Power Series Methods and Applications to Approximation Theory. (4th April 2019) - Ünver, Mehmet; Orhan, Cihan
Abstract: In this article we introduce the concepts of P p -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.