A certain class of equi-statistical convergence in the sense of the deferred power-series method

Date

2023

Authors

Srivastava, Hari Mohan
Jena, Bidu Bhusan
Paikray, Susanta Kumar

Journal Title

Journal ISSN

Volume Title

Publisher

Axioms

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.

Description

Keywords

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

Citation

Srivastava, H. M., Jena, B. B., & Paikray, S. K. (2023). A certain class of equi-statistical convergence in the sense of the deferred power-series method. Axioms, 12(10), 964. https://doi.org/10.3390/axioms12100964