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

Zeng, Xiaoming
Piriou, Alain

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Publication date

December 1998

DOI

10.1006/jath.1997.3227

Publisher

Academic Press.

ISSN

0021-9045

Abstract

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

Abstract

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

Abstract

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