Statistical deferred Cesàro summability and its applications to approximation theorems

Abstract

Statistical (C,1) summability and a Korovkin type approximation theorem has been proved by Mohiuddine et al. [20] (see [S. A. Mohiuddine, A. Alotaibi and M. Mursaleen, Statistical summability (C,1) and a Korovkin type approximation theorem, J. Inequal. Appl. 2012 (2012), Article ID 172, 1-8). In this paper, we apply statistical deferred Ces?ro summability method to prove a Korovkin type approximation theorem for the set of functions 1, e-x and e-2x defined on a Banach space C[0;1) and demonstrate that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. We also establish a result for the rate of statistical deferred Ces?ro summability method. Some interesting examples are also discussed here in support of our definitions and results.