@Article{ATA-40-381,
author = {Das , A. A.Mishra , Vishnu NarayanPaikray , S. K. and Parida , P.},
title = {A Certain Class of Equi-Statistical Convergence Based on $(p, q)$-integers via Deferred Nörlund Mean and Related Approximation Theorems},
journal = {Analysis in Theory and Applications},
year = {2025},
volume = {40},
number = {4},
pages = {381--404},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2018-0018},
url = {http://global-sci.org/intro/article_detail/ata/23861.html}
}