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Keywords:
Meyer-König and Zeller operator; function of two variables; approximation theorem
Meyer-König and Zeller operator; function of two variables; approximation theorem
Summary:
This paper is motivated by Kirov results on generalized Bernstein polynomials given in (Kirov, G. H., A generalization of the Bernstein polynomials, Math. Balk. New Ser. bf 6 (1992), 147–153.). We introduce certain modified Meyer-König and Zeller operators in the space of differentiable functions of two variables and we study approximation properties for them. Some approximation properties of the Meyer-König and Zeller operators of differentiable functions of one variable are given in (Rempulska, L., Tomczak, K., On certain modified Meyer-König and Zeller operators, Grant PB-43-71/2004.) and (Rempulska, L., Skorupka, M., On strong approximation by modified Meyer-König and Zeller operators, Tamkang J. Math. (in print).).
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