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Russian Mathematical Surveys, 2019, Volume 74, Issue 5, Pages 775–849
DOI: https://doi.org/10.1070/RM9839 (Mi rm9839) 		 
This article is cited in 22 scientific papers (total in 22 papers)

Chebyshev centres, Jung constants, and their applications

A. R. Alimovab, I. G. Tsar'kova

a Faculty of Mechanics and Mathematics, Moscow State University
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (1210 kB) Citations (22) Russian version article
References:
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DOI: https://doi.org/10.1070/RM9839
Abstract: The approximation of concrete function classes is the most common subject in the theory of approximations of functions. An important particular case of this is the problem of the Chebyshev centre and radius. As it turns out, this problem is not only a special case of the Kolmogorov width problem, but it is also related in a mysterious way to other important characteristics and results in the theory of functions and other more general branches of analysis and geometry. The aim of the present study is to give a survey of the current state of this problem and to discuss its possible applications.
Bibliography: 169 titles.
Keywords: Chebyshev centre, Chebyshev-centre map, Chebyshev net, Chebyshev point, Jung constant, fixed point theorem, normal structure coefficient.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00332
Ministry of Education and Science of the Russian Federation НШ 6222.2018.1
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 19-01-00332) and the Programme for State Support of Leading Scientific Schools of the President of the Russian Federation (project no. НШ 6222.2018.1).
Received: 25.06.2018
Revised: 22.02.2019
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
MSC: Primary 41A28, 41A65; Secondary 41A46, 46B20, 54C60, 54C65
Language: English
Original paper language: Russian
Citation: A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
Citation in format AMSBIB
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\vol 74
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\pages 775--849
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    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:83
    First page:44
     
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