Turkish Journal of Mathematics

Abstract: In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version. We also obtain a Voronovskaya-type theorem \ and some differential properties for sequences of positive linear operators constructed by means of the Bernstein polynomials of two variables.

Key Words: A-Statistical convergence of double sequence, Korovkin-type approximation theorem, Bernstein polynomials, Voronovskaya-type theorem.