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Russian Mathematical Surveys, 2019, Volume 74, Issue 5, Pages 775–849
DOI: https://doi.org/10.1070/RM9839
(Mi rm9839)
 

This article is cited in 23 scientific papers (total in 23 papers)

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
References:
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).
Received: 25.06.2018
Revised: 22.02.2019
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
MSC: Primary 41A28, 41A65; Secondary 41A46, 46B20, 54C60, 54C65
Language: English
Original paper language: Russian
Citation: A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
Citation in format AMSBIB
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\jour Russian Math. Surveys
\yr 2019
\vol 74
\issue 5
\pages 775--849
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Linking options:
  • https://www.mathnet.ru/eng/rm9839
  • https://doi.org/10.1070/RM9839
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  • This publication is cited in the following 23 articles:
    1. Tamim Aziz, Sanjoy Ghosal, “f -rough Cauchy sequences”, Quaestiones Mathematicae, 2025, 1  crossref
    2. Teena Thomas, “On property-(P1)(P1) and semi-continuity properties of restricted Chebyshev-center maps in -direct sums”, J Anal, 32:2 (2024), 681  crossref  mathscinet
    3. Evgeniǐ Vitalievich Nikitenko, Yuriǐ Gennadievich Nikonorov, “The Extreme Polygons for the Self Chebyshev Radius of the Boundary”, SScMath, 60:4 (2024), 193  crossref
    4. O. S. Malysheva, “Estimates of modified (Eucledean) Gromov–Hausdorff distance”, Moscow University Mathematics Bulletin, 79:4 (2024), 201–205  mathnet  crossref  crossref  elib
    5. Žiga Virk, “Contractibility of the Rips complexes of Integer lattices via local domination”, Trans. Amer. Math. Soc., 2024  crossref
    6. I. Ftouhi, E. Zuazua, “Optimal design of sensors via geometric criteria”, J. Geom. Anal., 33:8 (2023), 253  crossref  mathscinet
    7. I. G. Tsar'kov, “Estimates of the Chebyshev radius in terms of the MAX-metric function and the MAX-projection operator”, Russ. J. Math. Phys., 30:1 (2023), 128  crossref  mathscinet
    8. G. G. Braichev, B. N. Khabibullin, V. B. Sherstyukov, “Sylvester problem, coverings by shifts, and uniqueness theorems for entire functions”, Ufa Math. J., 15:4 (2023), 31–41  mathnet  crossref
    9. F. E. Levis, C. V. Ridolfi, L. Zabala, “Strong uniqueness and alternation theorems for relative Chebyshev centers”, Journal of Approximation Theory, 293 (2023), 105917  crossref  mathscinet  zmath
    10. S. Daptari, T. Paul, “On property-(R1)(R1) and relative Chebyshev centres in Banach spaces”, Numer. Funct. Anal. Optim., 43:4 (2022), 486–495  crossref  mathscinet  isi  scopus
    11. G. Z. Chelidze, A. N. Danelia, M. Z. Suladze, “On the Chebyshev Center and the Nonemptiness of the Intersection of Nested Sets”, Math. Notes, 111:3 (2022), 478–483  mathnet  crossref  crossref  mathscinet
    12. M. V. Balashov, “Covering a Set by a Convex Compactum: Error Estimates and Computation”, Math. Notes, 112:3 (2022), 349–359  mathnet  crossref  crossref  mathscinet
    13. I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Sb. Math., 213:10 (2022), 1444–1469  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. A. R. Alimov, “Monotone path-connectedness of strict suns”, Lobachevskii J. Math., 43:3 (2022), 519–527  crossref  mathscinet
    15. I. G. Tsar'kov, “Properties of monotone path-connected sets”, Izv. Math., 85:2 (2021), 306–331  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    16. I. G. Tsar'kov, “Properties of Monotone Connected Sets”, Math. Notes, 109:5 (2021), 819–827  mathnet  crossref  crossref  isi  elib
    17. V. Balestro, H. Martini, Yu. Nikonorov, Yu. Nikonorova, “Extremal problems for convex curves with a given self Chebyshev radius”, Result. Math., 76:2 (2021), 87, 13 pp.  crossref  mathscinet  zmath  isi  scopus
    18. A. R. Alimov, “Solarity of Chebyshev sets in dual spaces and uniquely remotal sets”, Lobachevskii J. Math., 42:4 (2021), 785–790  mathnet  crossref  mathscinet  zmath  isi  scopus
    19. E. V. Shchepin, “On the Sierpiński–Knopp curve”, Russian Math. Surveys, 75:2 (2020), 377–379  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Algoritmy minimizatsii khausdorfova otkloneniya vypuklogo kompakta ot nabora podvizhnykh vypuklykh mnogougolnikov”, Chelyab. fiz.-matem. zhurn., 5:2 (2020), 218–232  mathnet  crossref
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