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Zbl 1222.41007
Anastassiou, G.A.; Mursaleen, M.; Mohiuddine, S.A.
Some approximation theorems for functions of two variables through almost convergence of double sequences. (English)
[J] J. Comput. Anal. Appl. 13, No. 1, 37-46 (2011). ISSN 1521-1398; ISSN 1572-9206/e

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.

MSC 2000:: *41A10 Approximation by polynomials
41A25 Degree of approximation, etc.
41A36 Approximation by positive operators
40A05 Convergence of series and sequences
40A30 Convergence of series and sequences of functions

Keywords: double sequence; almost convergence; Korovkin type approximation theorem

Citations: Zbl 0675.40004

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