A Certain Class of Equi-Statistical Convergence in the Sense of the Deferred Power-Series Method

Abstract

In this paper, we expose the ideas of point-wise statistical convergence, equi-statistical convergence and uniform statistical convergence in the sense of the deferred power-series method. We then propose a relation connecting them, which is followed by several illustrative examples. Moreover, as an application viewpoint, we establish an approximation theorem based upon our proposed method for equi-statistical convergence of sequences of positive linear operators. Finally, we estimate the equi-statistical rates of convergence for the effectiveness of the results presented in our study.

Keywords

• statistical convergence
• deferred power-series method
• Cesàro summability
• Korovkin-type theorem
• bernstein polynomials
• rate of convergence