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.


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