TY - JOUR
T1 - A Certain Class of Equi-Statistical Convergence Based on $(p, q)$-integers via Deferred Nörlund Mean and Related Approximation Theorems
AU - Das , A. A.
AU - Mishra , Vishnu Narayan
AU - Paikray , S. K.
AU - Parida , P.
JO - Analysis in Theory and Applications
VL - 4
SP - 381
EP - 404
PY - 2025
DA - 2025/02
SN - 40
DO - http://doi.org/10.4208/ata.OA-2018-0018
UR - https://global-sci.org/intro/article_detail/ata/23861.html
KW - Statistical convergence, $(p, q)$-integers, deferred Nörlund summability, $\varphi^{p,q}_n$-equi-statistical convergence, rate of convergence and Korovkin type approximation theorems.
AB - <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>