Chebyshev centres, Jung constants, and their applications

Author:

Alimov A. R.,Tsar’kov I. G.

Abstract

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.

Funder

Russian Foundation for Basic Research

Ministry of Education and Science of the Russian Federation

Publisher

IOP Publishing

Subject

General Mathematics

Cited by 17 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The Extreme Polygons for the Self Chebyshev Radius of the Boundary;Studia Scientiarum Mathematicarum Hungarica;2024-01-29

2. On The Farthest Point Problem In Hilbert Spaces;European Journal of Pure and Applied Mathematics;2023-10-30

3. Strong uniqueness and alternation theorems for relative Chebyshev centers;Journal of Approximation Theory;2023-09

4. Estimates of the Chebyshev Radius in Terms of the MAX-Metric Function and the MAX-Projection Operator;Russian Journal of Mathematical Physics;2023-03

5. Sylvester problem, coverings by shifts, and uniqueness theorems for entire functions;Ufa Mathematical Journal;2023

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