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POINTWISE APPROXIMATION BY BERNSTEIN POLYNOMIALS

Part of: Approximations and expansions

Published online by Cambridge University Press:  06 February 2012

GANCHO TACHEV
GANCHO TACHEV*
Affiliation:
Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, BG-1046, Sofia, Bulgaria (email: gtt_fte@uacg.acad.bg)
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Abstract

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We improve the degree of pointwise approximation of continuous functions f(x) by Bernstein operators, when x is close to the endpoints of [0,1]. We apply the new estimate to establish upper and lower pointwise estimates for the test function g(x)=xlog (x)+(1−x)log (1−x). At the end we prove a general statement for pointwise approximation by Bernstein operators.

Keywords

Bernstein polynomialsDirect theoremsDitzian–Totik moduli of smoothness

MSC classification

Secondary: 41A10: Approximation by polynomials 41A25: Rate of convergence, degree of approximation 41A36: Approximation by positive operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 3 , June 2012 , pp. 353 - 358
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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