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

By Mehmet Ünver, Cihan Orhan. Numerical Functional Analysis and Optimization, 2019

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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.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d09f4dc1e2d3f6579acf9f130e37db45e1608c81