Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T10:02:52.591Z Has data issue: false hasContentIssue false
  • English
  • Français

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])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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