Statistical (C, 1) (E, 1) Summability and Korovkin's Theorem

Abstract

Korovkin-type approximation theory usually deals with convergence analysis for sequences of positive operators. This approximation theorem was extended to more general space of sequences via different way such as statistical convergence, summation processes. In this work, we introduce a new type of statistical product summability, that is, statistical (C, 1) (E, 1) summability and further apply our new product summability method to prove Korovkin type theorem. Furthermore, we present a rate of convergence which is uniform in Korovkin type theorem by statistical (C, 1) (E, 1) summability.