A new approach to statistical Riemann-Stieltjes integrals

Abstract

This paper aims to introduce various concepts of statistical Riemann-Stieltjes sum via the deferred Nörlund summability mean for the sequence of functions as well as the sequence of distribution functions. We first establish some fundamental limit theorems for statistical Riemann-Stieltjes sum in the sequence space. Then over the probability sequence space, we establish some more advanced results. Finally, over both the spaces we establish some inclusion theorems via our proposed mean in association with statistical Riemann-Stieltjes integral.