Deferred Norlund statistical convergence in probability, mean and distribution for sequences of random variables

TL;DR

This paper introduces deferred N"{o}rlund statistical convergence concepts for sequences of random variables across probability, mean, and distribution, establishing new theorems and demonstrating their effectiveness with examples.

Contribution

It presents novel deferred N"{o}rlund statistical convergence definitions and Korovkin type theorems for random variables, expanding the theoretical framework.

Findings

New definitions of deferred N"{o}rlund statistical convergence in probability, mean, and distribution.

Establishment of Korovkin type theorems using these new convergence concepts.

Examples demonstrating the applicability and effectiveness of the theoretical results.

Abstract

We introduce and study deferred N\"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin type theorems for the sequence of random variables via deferred N\"{o}rlund statistically convergence and present compelling examples to demonstrate the effectiveness of the results.