Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems

Abstract

In this paper, we propose to investigate a new weighted statistical convergence by applying the Norlund–Cesaro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem.