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On the Rate of Convergence of Two Bernstein–Bézier Type Operators for Bounded Variation Functions

Authors:	Xiaoming Zeng Alain Piriou

Affiliation:	^aDepartment of Mathematics, Xiamen University, Xiamen, Fujian, 361005, People's Republic of China^f1;^bLaboratoire de Mathématiques, Université de Nice–Sophia Antipolis, URA-CNRS No. 168, Parc Valrose, F-06108, Nice Cedex 2, France

Abstract:	In this paper we study the rate of convergence of two Bernstein–Bézier type operatorsB^(α)_nandL^(α)_nfor bounded variation functions. By means of construction of suitable functions and the method of Bojanic and Vuillemier (J. Approx. Theory31(1981), 67–79), using some results of probability theory, we obtain asymptotically optimal estimations ofB^(α)_nandL^(α)_nfor bounded variation functions at points of continuity and points of discontinuity.

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