A Korovkin's type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallee Poussin mean

The main object of this paper is to prove a Korovkin type theorem for the test functions 1, cos x, sin x in the space C-2 pi(R) of all continuous 2 pi-periodic functions on the real line E. Our analysis is based upon the statistical summability involving the idea of the generalized de In Vallee Poussin mean. We also investigate the rate of the de la Vallee Poussin statistical summability of positive linear operators in the space C-2 pi(R). Finally, we provide an interesting illustrative example in support of our result. (C) 2013 Elsevier Inc. All rights reserved.