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