\(q\)-Bernstein polynomials and their iterates.
type: Item
instance of: scholarly article
title: \(q\)-Bernstein polynomials and their iterates.
zbMATH Open document ID: 1093.41013
DOI: 10.1016/S0021-9045(03)00104-7
author: Sofiya Ostrovska
published in: Journal of Approximation Theory
publication date: 2003-08-25T00:00:00Z
review text: \(q\)-Bernstein polynomials have been introduced by \textit{G. M. Phillips} [in Numerical Analysis: A. R. Mitchell 75th Birthday Volume, World Scientific, Singapore, 263--269 (1996)]. For \(q=1\) they reduce to the classical Bernstein polynomials. When \(q\) is in \((0,1)\), the corresponding linear operators are positive; several papers deal with this case. When \(q>1\), the positivity fails. The author shows that in this case the approximation properties of \(q\)-Bernstein polynomials may be better than in the case \(q<1\) or \(q=1\); in particular, for entire functions the rate of convergence is exponential. The iterates of \(q\)-Bernstein operators are also investigated. For \(q>1\), the situation is very similar to the classical case \(q=1\); for \(0<q<1\), it is essentially different.
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 33D45
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 1970539
zbMATH Keywords: \(q\)-Bernstein polynomials
zbMATH Keywords: convergence
zbMATH Keywords: iterates
reviewed by: Ioan Raşa
MaRDI profile type: Publication
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full work available at URL: s0021-9045(03)00104-7
OpenAlex ID: W1971507256
description: scientific article; zbMATH DE number 1970539