Statistical Deferred Cesaro 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. [Journal of Inequalities and Applications 2012, 2012:172]. In this paper, we apply statistical deferred Cesaro summability method to prove a Korovkin type approximation theorem for the set of functions
{1, e^{-x}, e^{-2x}} defined on a Banach space C[0,\infty) and demonstrate that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. We also establish a result for rate of statistical deferred Cesaro summability method. Some interesting examples are also discussed here in support of our definitions and results.