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Some approximation theorems for functions of two variables through almost convergence of double sequences. (English) Zbl 1222.41007

Summary: The idea of almost convergence for double sequences was introduced by F. Móricz and B. E. Rhoades [Math. Proc. Camb. Philos. Soc. 104, No. 2, 283–294 (1988; Zbl 0675.40004)]. In this paper, we use this concept to prove a Korovkin type approximation theorem for functions of two variables along with a supporting example. Further, we present some consequences of our main theorem.

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
40A05 Convergence and divergence of series and sequences
40A30 Convergence and divergence of series and sequences of functions

Citations:

Zbl 0675.40004
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