On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions. II
type: Item
instance of: scholarly article
title: On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions. II
zbMATH Open document ID: 0963.41011
published in: Journal of Approximation Theory
publication date: 2001-01-04T00:00:00Z
review text: For Bernstein-Bézier type operators \(B_n^{(\alpha)}\), \(n \in \mathbb{N}_0\), \(0<\alpha<1\) and Bernstein-Kantorovich-Bézier type operators \(L_n^{(\alpha)}\), \(n\in\mathbb{N}_0\), \(0<\alpha<1\) the pointwise rate of convergence of \(B_n^{(\alpha)}f\) and \(L_n^{(\alpha)}f\) respectively for \(n\to \infty\) to functions \(f\in BV[0,1]\) is studied. The estimates turn out to be asymptotically optimal. In a first paper \textit{X. Zeng}, and \textit{A. Piriou} [J. Approximation Theory 95, No. 3, 369-387 (1998; Zbl 0918.41016) the case \(\alpha\geq 1\) has been treated.
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 1496282
zbMATH Keywords: Bernstein-Bézier type operators
zbMATH Keywords: Bernstein-Kantorovich-Bézier type operators
author: Xiao-Ming Zeng
reviewed by: Manfred Wolfgang Müller
MaRDI profile type: Publication
full work available at URL: jath.2000.3451
OpenAlex ID: W4234779141
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DOI: 10.1006/JATH.2000.3451
description: scientific article; zbMATH DE number 1496282