### Equi-Statistical Convergence of a Sequence of Distribution Functions via Deferred N\"{o}rlund Summability Mean and Associated Approximation Theorems

#### Abstract

In this paper, the notion of statistical point-wise convergence,

equi-statistical convergence and statistical uniform convergence

of a sequence of distribution functions via the deferred

N\"{o}rlund summability mean has been introduced, and accordingly

an inclusion relation between these interesting notions is

established. Moreover, as an application point of view, a new

Korovkin-type approximation theorem is proved via the deferred

N\"{o}rlund equi-statistical convergence for the sequence of

distribution functions. Also, some illustrative examples are

considered to justify that the proposed theorem is a nontrivial

extension of some well established Korovkin-type approximation

theorems for sequence of real-valued functions. Finally, a number

of interesting cases are highlighted in support of the definitions

and outcomes.

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