This article is cited in 2 papers

Best Approximations of Convex Compact Sets by Balls in the Hausdorff Metric

E. N. Sosov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: We deduce 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. We prove that the set $\chi[M]$ of centers of closed balls approximating a convex compact set in the Hausdorff metric in the best possible way is nonempty $X[M]$ and is contained in $M$. Some other properties of $\chi[M]$ also are investigated.

UDC: 515.124.4

Received: 21.02.2003
Revised: 10.06.2003

DOI: 10.4213/mzm102

 English version: Mathematical Notes, 2004, 76:2, 209–218

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