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Sbornik: Mathematics, 2000, Volume 191, Issue 10, Pages 1433–1458
DOI: https://doi.org/10.1070/sm2000v191n10ABEH000513 (Mi sm513) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Uniform estimate of a compact convex set by a ball in an arbitrary norm

S. I. Dudov, I. V. Zlatorunskaya

Saratov State University named after N. G. Chernyshevsky
English version PDF (263 kB) Citations (16)
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DOI: https://doi.org/10.1070/sm2000v191n10ABEH000513
Abstract: The problem of the best uniform approximation of a compact convex set by a ball with respect to an arbitrary norm in the Hausdorff metric corresponding to that norm is considered.
The question is reduced to a convex programming problem, which can be studied by means of convex analysis. Necessary and sufficient conditions for the solubility of this problem are obtained and several properties of its solution are described. It is proved, in particular, that the centre of at least one ball of best approximation lies in the compact set under consideration; in addition, conditions ensuring that the centres of all balls of best approximation lie in this compact set and a condition for unique solubility are obtained.
Received: 26.07.1999
Russian version:
Matematicheskii Sbornik, 2000, Volume 191, Number 10, Pages 13–38
DOI: https://doi.org/10.4213/sm513
Bibliographic databases:
UDC: 517.982.256+519.853.3
MSC: Primary 52A27; Secondary 49J52, 90C25
Language: English
Original paper language: Russian
Citation: S. I. Dudov, I. V. Zlatorunskaya, “Uniform estimate of a compact convex set by a ball in an arbitrary norm”, Mat. Sb., 191:10 (2000), 13–38; Sb. Math., 191:10 (2000), 1433–1458
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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