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A Certain Class of Equi-Statistical Convergence Based on (p,q)-integers via Deferred Nörlund Mean and Related Approximation Theorems

A Certain Class of Equi-Statistical Convergence Based on $(p, q)$-integers via Deferred Nörlund Mean and Related Approximation Theorems

Year:    2024

Author:    A. A. Das, Vishnu Narayan Mishra, S. K. Paikray, P. Parida

Analysis in Theory and Applications, Vol. 40 (2024), Iss. 4 : pp. 381–404

Abstract

The concept of equi-statistical convergence is more general than that of the well-established statistical uniform convergence. In this paper, we have introduced the idea of equi-statistical convergence, statistical point-wise convergence and statistical uniform convergence under the difference operator including (p,q)-integers via deferred Nörlund statistical convergence so as to build up a few inclusion relations between them. We have likewise presented the notion of the deferred weighted (Nörlund type) equi-statistical convergence (presumably new) in view of difference sequence of order r based on (p,q)-integers to demonstrate a Korovkin type approximation theorem and proved that our theorem is a generalization (non-trivial) of some well-established Korovkin type approximation theorems which were demonstrated by earlier authors. Eventually, we set up various fascinating examples in connection with our definitions and results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2018-0018

Analysis in Theory and Applications, Vol. 40 (2024), Iss. 4 : pp. 381–404

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Statistical convergence $(p q)$-integers deferred Nörlund summability $\varphi^{p q}_n$-equistatistical convergence rate of convergence and Korovkin type approximation theorems. q}_n$-equi-statistical convergence

Author Details

A. A. Das

Vishnu Narayan Mishra

S. K. Paikray

P. Parida