Approximation of continuous periodic functions via statistical convergence

In this work, we give a nontrivial generalization of the classical Korovkin approximation theorem by using the concept of A-statistical convergence, which is a regular (nonmatrix) summability method, for sequences of positive linear operators defined on the space of all real-valued continuous and 2 pi periodic functions on the real m-dimensional space. Furthermore, in the case of m = 2, we display an application which shows that our result is stronger than the classical approximation. (c) 2006 Elsevier Ltd. All rights reserved.