A New Class of Korovkin-Type Approximation Theorems Based on Equi-Statistical Convergence of Double Sequences

Abstract

In this article, we explore the concepts of point-wise statistical convergence, equi-statistical convergence, and uniform statistical convergence for sequences of functions of two variables, employing the deferred power-series method. We then demonstrate the inclusion relationships among these concepts, supplemented by several illustrative numerical examples. Furthermore, from an application perspective, we introduce a Korovkin-type theorem that utilizes our proposed method to examine the equi-statistical convergence of sequences of positive linear operators. Additionally, we consider an example involving the Meyer-K\"{o}nig and Zeller operator and use MATLAB software to illustrate the convergence behavior of the operator. Finally, we provide an estimation of the equi-statistical convergence rates to assess the effectiveness of the findings in our research.