Equi-Statistical Convergence of a Sequence of Distribution Functions via Deferred Norlund Summability Mean and Associated Approximation Theorems

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 Norlund 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 Norlund 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.