Deferred statistical convergence of ????-transformation of real valued sequences

Abstract

This paper introduces the concept of deferred statistical ????-convergence, which combines the deferred density of subsets of natural numbers with an infinite regular matrix ????=(a_mk). We explore the fundamental properties of deferred statistical ????-convergent sequences and investigate the relationships between deferred statistical ????-convergence, strongly deferred statistical ????-convergence, and deferred statistical convergence. Additionally, we present a Korovkin-type approximation theorem utilizing deferred statistical ????-convergence and provide a counter-example to demonstrate its limitations. The findings contribute to the understanding of statistical convergence, deferred statistical convergence, matrix transformations, and the development of Korovkin-type theorems.