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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 {\it F. Móricz} and {\it 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.

41A10Approximation by polynomials
41A25Rate of convergence, degree of approximation
41A36Approximation by positive operators
40A05Convergence and divergence of series and sequences
40A30Convergence and divergence of series and sequences of functions