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

Abstract

The main object of this paper is to prove a Korovkin type theorem for the test functions 1, cosx,sinx in the space C2π(R) of all continuous 2π-periodic functions on the real line R. Our analysis is based upon the statistical summability involving the idea of the generalized de la Vallée Poussin mean. We also investigate the rate of the de la Vallée Poussin statistical summability of positive linear operators in the space C2π(R). Finally, we provide an interesting illustrative example in support of our result.