On the Rate of Convergence of Two Bernstein–Bézier Type Operators for Bounded Variation Functions |
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Authors: | Xiaoming Zeng Alain Piriou |
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Affiliation: | aDepartment of Mathematics, Xiamen University, Xiamen, Fujian, 361005, People's Republic of Chinaf1;bLaboratoire de Mathématiques, Université de Nice–Sophia Antipolis, URA-CNRS No. 168, Parc Valrose, F-06108, Nice Cedex 2, France |
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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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