On Certain Statistical Convergence Criteria for Martingale Sequences via Deferred Ces`aro Mean with Some Applications

Abstract

In this paper, we investigate and study various new notions of statistical convergence criteria of martingale sequences via deferred Ces`aro mean. We then establish several results concerning the relation among these beautiful and potentially useful concepts. Moreover, our proposed techniques contributed to finding several new approximation results of the Korovkin-type for martingale sequences over complete normed linear spaces. We also present some concrete examples to establish the stronger side of our results.