Chebyshev centres, Jung constants, and their applications

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, bu...

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Bibliographic Details
Published inRussian mathematical surveys Vol. 74; no. 5; pp. 775 - 849
Main Authors Alimov, A. R., Tsar'kov, I. G.
Format Journal Article
LanguageEnglish
Published London London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences 01.10.2019
IOP Publishing
Subjects
Chebyshev approximation
Chebyshev centre
Chebyshev net
Chebyshev point
Chebyshev-centre map
fixed point theorem
Jung constant
normal structure coefficient
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0036-0279
1468-4829
DOI:10.1070/RM9839