Deferred statistical convergence of A-transformation of real valued sequences

Abstract

This paper introduces the concept of deferred statistical A-convergence, which combines the de-ferred density of subsets of natural numbers with an infinite regular matrix A= (amk). We explore the funda-mental properties of deferred statistical A-convergent sequences and investigate the relationships between deferred statistical A-convergence, strongly deferred statistical A-convergence, and deferred statistical con-vergence. Additionally, we present a Korovkin-type approximation theorem utilizing deferred statistical A-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.