MMN-3624
Deferred Cesaro statistical convergence of martingale sequence and Korovkin-type approximation theorems
H. M. Srivastava; Bidu Bhusan Jena; Susanta Kumar Paikray;Abstract
In the present paper, we introduce and study the concepts of
statistical convergence and statistical summability for martingale
sequences of random variables via deferred Ces\`{a}ro mean. We
then establish an inclusion theorem concerning the relation
between these two beautiful and potentially useful concepts. Also,
based upon our proposed notions, we state and prove new
Korovkin-type approximation theorems with algebraic test functions
for a martingale sequence over a Banach space. Moreover, we
demonstrate that our theorems effectively extend and improve most
(if not all) of the previously existing results (in statistical
and classical versions). Finally, by using the generalized
Bernstein polynomials, we present an illustrative example of a
martingale sequence in order to demonstrate that our established
theorems are stronger than their traditional and statistical
versions.
Vol. 23 (2022), No. 1, pp. 443-456
DOI: 10.18514/MMN.2022.3624