Best approximations of convex compact sets by balls in the Hausdorff metric
type: Item
instance of: scholarly article
title: Best approximations of convex compact sets by balls in the Hausdorff metric
zbMATH Open document ID: 1095.41019
published in: Mathematical Notes
publication date: 2004-12-07T00:00:00Z
review text: An upper bound for the Hausdorff distance between a nonempty bounded set and the set of all closed balls in a strictly convex straight geodesic space \(X\) of nonnegative curvature is obtained. It is also proved that the set \(\chi[M]\) of centers of the closed balls approximating a convex compact set \(M\) is nonempty and contained in \(M\). The authors also study some other properties of \(\chi[M]\). These results extend some results due to \textit{S. I. Dudov} and \textit{I. V. Zlatorunskaya} [Sb. Math. 191, No. 10, 1433--1458 (2000); translation from Mat. Sb. 191, No. 10, 13--38 (2000; Zbl 0981.52005)] to the case of a strictly convex straight geodesic space.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 2121460
zbMATH Keywords: geodesic metric space
zbMATH Keywords: bounded set
zbMATH Keywords: Hausdorff metric
author: Evgenii N. Sosov
MaRDI profile type: Publication
full work available at URL: b:matn.0000036759.76369.0b
OpenAlex ID: W1965282267
DOI: 10.1023/B:MATN.0000036759.76369.0B
description: scientific article; zbMATH DE number 2121460