Statistical Deferred Cesàro Summability and Its Applications to Approximation Theorems


Bidu Bhusan Jena, Susanta Kumar Paikray, Umakanta Misra




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 Cesàro 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, ∞) 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 Cesàro summability method. Some interesting examples are also discussed here in support of our definitions and results.