On Statistical Riemann-Stieltjes Integrablility and Deferred Cesàro Summabilit

Abstract

In this paper, we first introduce and study the notion of statistical Riemann-Stieltjes sum for the sequence of functions and establish some elementary results based on this notion. Subsequently, we extend this notion to the probability space and demonstrate some new results for sequence of distribution functions. Furthermore, we suggest the deferred Cesàro summability method for Riemann-Stieltjes sum. We then establish various inclusion theorems based on our proposed methods in association with the Riemann-Stieltjes sum for the sequence of usual functions as well as distribution functions in Rⁿ.