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Matematicheskie Zametki, 2004, Volume 76, Issue 2, Pages 226–236
DOI: https://doi.org/10.4213/mzm102
(Mi mzm102)
 

This article is cited in 2 scientific papers (total 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
Full-text PDF (195 kB) Citations (2)
References:
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.
Received: 21.02.2003
Revised: 10.06.2003
English version:
Mathematical Notes, 2004, Volume 76, Issue 2, Pages 209–218
DOI: https://doi.org/10.1023/B:MATN.0000036759.76369.0b
Bibliographic databases:
UDC: 515.124.4
Language: Russian
Citation: E. N. Sosov, “Best Approximations of Convex Compact Sets by Balls in the Hausdorff Metric”, Mat. Zametki, 76:2 (2004), 226–236; Math. Notes, 76:2 (2004), 209–218
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm102
  • https://www.mathnet.ru/eng/mzm/v76/i2/p226
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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