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Direct and converse results for q-Bernstein operators

Part of: Approximations and expansions

Published online by Cambridge University Press:  28 May 2009

Zoltán Finta
Zoltán Finta
Affiliation:
Department of Mathematics, Babeş-Bolyai University, Mihail Kogălniceanu nr. 1, RO 400084, Cluj-Napoca, Romania; Email: ([email protected])
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Abstract

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Direct and converse theorems are established for the q-Bernstein polynomials introduced by G. M. Phillips. The direct approximation theorems are given for the second-order Ditzian–Totik modulus of smoothness. The converse results are theorems of Berens–Lorentz type.

Keywords

q-Bernstein polynomialsK-functionalDitzian–Totik modulus of smoothnessBerens–Lorentz-type theorem

MSC classification

Secondary: 41A10: Approximation by polynomials 41A25: Rate of convergence, degree of approximation 41A27: Inverse theorems 41A36: Approximation by positive operators
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 2 , June 2009 , pp. 339 - 349
Copyright
Copyright © Edinburgh Mathematical Society 2009