Statistical Voronoi mean and applications to approximation theorems

Abstract

In this paper, we give statistical Voronoi mean which is a new statistical summability method, is not need to be regular and positive. We prove a Korovkin type approximation theorem via this method that covers many important summability methods scattered in the literature. Also, we demonstrate that our theorem is stronger than proven by earlier authors with an interesting application. Finally, we establish the rate of convergence.