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
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.
Chebyshev centre, Chebyshev-centre map, Chebyshev net, Chebyshev point, Jung constant, fixed point theorem, normal structure coefficient.
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Russian Mathematical Surveys, 2019, 74:5, 775–849
MSC: Primary 41A28, 41A65; Secondary 41A46, 46B20, 54C60, 54C65
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
\by A.~R.~Alimov, I.~G.~Tsar'kov
\paper Chebyshev centres, Jung constants, and their applications
\jour Uspekhi Mat. Nauk
\jour Russian Math. Surveys
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