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Abstract: 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 denned on the space of all real-valued continuous and 2π 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. [Copyright &y& Elsevier]