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Direct and converse results for q-Bernstein operators

Published online by Cambridge University Press:  28 May 2009

Zoltán Finta
Affiliation:
Department of Mathematics, Babeş-Bolyai University, Mihail Kogălniceanu nr. 1, RO 400084, Cluj-Napoca, Romania; Email: (fzoltan@math.ubbcluj.ro)
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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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2009