Weighted approximation by multidimensional Bernstein operators
type: Item
instance of: scholarly article
title: Weighted approximation by multidimensional Bernstein operators
zbMATH Open document ID: 0809.41019
author: Ding-Xuan Zhou
published in: Journal of Approximation Theory
publication date: 1994-07-03T00:00:00Z
review text: The purpose of this paper is to give inverse theorems for univariate and multivariate Bernstein operators with some Jacobi weights. The main result in the univariate case is an analogue of the inverse theorem for weighted approximation by Kantorovich operators proved by \textit{Z. Ditzian} and \textit{V. Totik}, Moduli of smoothness (1987; Zbl 0666.41001). In the multivariate case few inverse results are known. The first result of this kind was obtained by \textit{Z. Ditzian}, Inverse theorems for multidimensional Bernstein operators, Pac. J. Math. 121, 293-319 (1986; Zbl 0581.41023)]. Here the author discusses the weighted approximation problem for multidimensional Bernstein operators.
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 575577
zbMATH Keywords: Jacobi weights
zbMATH Keywords: multidimension Bernstein operators
reviewed by: H. R. Dowson
MaRDI profile type: Publication
full work available at URL: jath.1994.1026
OpenAlex ID: W1970354588
DOI: 10.1006/JATH.1994.1026
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description: scientific article; zbMATH DE number 575577