Titlebook: Geometric Approximation Theory; Alexey R. Alimov,Igor’ G. Tsar’kov Book 2021 The Editor(s) (if applicable) and The Author(s), under exclus

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熔巖

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The Jung Constant,The Jung constant appears in many problems in various fields of mathematics. In the present chapter, we will give examples of such problems and present the available exact values of the Jung constant for several classical spaces.

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978-3-030-90953-6The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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https://doi.org/10.1007/978-981-19-4097-2owing fact important for applications: in corresponding spaces, a?nonconvex set cannot be a?Chebyshev set. As a?corollary, at some point either the existence or the uniqueness property is not satisfied. Results of this kind can be useful in solving extremal problems.

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斑駁

Ulrike Tikvah Kissmann,Joost‘van Loonr to show that a?Chebyshev set is convex, it suffices to prove its ‘solarity’ (in some sense or other) and then employ Theorem?. on the convexity of suns in smooth spaces (of course if the corresponding space is smooth).

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https://doi.org/10.1007/978-1-4842-3267-5al-valued functions, approximation by Chebyshev subspaces was found to be closely related to various problems in interpolation, uniqueness, and the number of zeros in nontrivial polynomials (the generalized Haar property). For vector-valued functions, the relation between such properties turned out to be less simple.