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Uspekhi Mat. Nauk, 2019, Volume 74, Issue 5(449), Pages 3–82 (Mi umn9839)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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).


DOI: https://doi.org/10.4213/rm9839

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English version:
Russian Mathematical Surveys, 2019, 74:5, 775–849

Bibliographic databases:

UDC: 517.982.256
MSC: Primary 41A28, 41A65; Secondary 41A46, 46B20, 54C60, 54C65
Received: 25.06.2018
Revised: 22.02.2019

Citation: A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Uspekhi Mat. Nauk, 74:5(449) (2019), 3–82; Russian Math. Surveys, 74:5 (2019), 775–849

Citation in format AMSBIB
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\by A.~R.~Alimov, I.~G.~Tsar'kov
\paper Chebyshev centres, Jung constants, and their applications
\jour Uspekhi Mat. Nauk
\yr 2019
\vol 74
\issue 5(449)
\pages 3--82
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3920426}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019RuMaS..74..775A}
\transl
\jour Russian Math. Surveys
\yr 2019
\vol 74
\issue 5
\pages 775--849
\crossref{https://doi.org/10.1070/RM9839}
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    This publication is cited in the following articles:
    1. E. V. Schepin, “O krivoi Serpinskogo–Knoppa”, UMN, 75:2(452) (2020), 191–192  mathnet  crossref
  • Успехи математических наук Russian Mathematical Surveys
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