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Korovkin type approximation theorem for functions of two variables in statistical sense. (English) Zbl 1185.41013

Summary: 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.

MSC:

41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
40A05 Convergence and divergence of series and sequences
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