MMN-3014
Product of statistical probability convergence and its applications to Korovkin-type theorem
Bidu Bhusan Jena; Susanta Kumar Paikray;Abstract
In the present work, we introduce and study the notion of statistical probability convergence for sequences of random variables as well as the concept of statistical convergence for sequences of real numbers, which are defined over a Banach space via product of deferred Ces\`{a}ro and deferred N\"{o}rlund
summability means. We first establish a theorem presenting a connection between them. Based upon our proposed methods, we then prove a Korovkin-type approximation theorem with algebraic test functions for a sequence of random variables on a Banach space and
demonstrate that our theorem effectively extends and improves most (if not all) of the previously existing results (in classical as well as statistical versions). Finally, an illustrative example is presented here by means of the generalized Meyer-K\"{o}nig and
Zeller operators of a sequence of random variables in order to demonstrate that our established theorem is stronger than its traditional and statistical versions.
Vol. 20 (2019), No. 2, pp. 969-984
DOI: 10.18514/MMN.2019.3014