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Korovkin type approximation theorems for \(\sigma\)-convergence of double sequences. (English) Zbl 1314.41003

It is recalled the convergence in Pringsheim’s sense and the \(\sigma\)-convergence of a double sequence. Using this last notion, Korovkin type approximation theorems are established for functions of two variables by using different sets of test functions. It is also proven that the new results are stronger than some other Korovkin type approximation theorems.

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
40A30 Convergence and divergence of series and sequences of functions
40G15 Summability methods using statistical convergence
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