Some remarks on relative Chebyshev centers
type: Item
instance of: scholarly article
title: Some remarks on relative Chebyshev centers
zbMATH Open document ID: 0876.41029
author: V. S. Balanganskij
published in: Journal of Approximation Theory
publication date: 1997-07-15T00:00:00Z
review text: Let \(X\) be a Hilbert space with \(F(X)\) as the set of all closed nonempty convex subsets of \(X\). Suppose that \(Y\), \(K\in F(X)\) and \(K\) is bounded. Then the author shows that the set of all relative Chebyshev centres of \(K\) with respect to \(Y\) is a subset of \(P_Y(K)\), where \(P_Y\) is the metric projection onto \(Y\). This extends an earlier result of \textit{D. Amir} and \textit{J. Mach} [J. Approximation Theory 40, 364-374 (1984; Zbl 0546.41029), Corollary 2.9], where \(K\) is assumed to be convex and compact. Necessary and sufficient conditions for relative Chebychev centres are also obtained.
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 1033757
zbMATH Keywords: relative Chebyshev centres
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
full work available at URL: jath.1996.3058
OpenAlex ID: W1978166870
cites work: Chebyshev centers in normed spaces
cites work: Q5513397
DOI: 10.1006/JATH.1996.3058
description: scientific article; zbMATH DE number 1033757