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Abstract. In this paper, we obtain a Korovkin type approximation theorem for double sequences of positive linear operators of two variables from H w (K) to C (K) via A-statistical convergence. Also, we construct an example such that our new approximation result works but its classical case does not work. Furthermore, we study the rates of A-statistical convergence by means of the modulus of continuity.

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ABSTRACT. Our primary interest in the present paper is to prove a Korovkintype approximation theorem for sequences of positive linear operators defined on the space of all real valued n-variate B-continuous functions on a compact subset of the real n-dimensional space via statistical convergence. Also, we display an example such that our method of convergence is stronger than the usual convergence.