A. R. Alimov, “The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$”, Funktsional. Anal. i Prilozhen., 39:1 (2005), 1–10; Funct. Anal. Appl., 39:1 (2005), 1

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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 1, Pages 1–10
DOI: https://doi.org/10.4213/faa27 (Mi faa27)

This article is cited in 11 scientific papers (total in 11 papers)

The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$

A. R. Alimov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (219 kB) Citations (11)

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DOI: https://doi.org/10.4213/faa27

Abstract: A subset $M$ of a normed linear space $X$ is called a Chebyshev set if each $x\in X$ has a unique nearest point in $M$. We characterize Chebyshev sets in $\ell^\infty(n)$ in geometric terms and study the approximative properties of sections of Chebyshev sets, suns, and strict suns in $\ell^\infty(n)$ by coordinate subspaces.

Keywords: Chebyshev set, sun, strict sun, best approximation.

Received: 27.02.2003

English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 1, Pages 1–8
DOI: https://doi.org/10.1007/s10688-005-0012-x

Bibliographic databases:

Document Type: Article

UDC: 517.982.256

Language: Russian

Citation: A. R. Alimov, “The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$”, Funktsional. Anal. i Prilozhen., 39:1 (2005), 1–10; Funct. Anal. Appl., 39:1 (2005), 1–8

Citation in format AMSBIB

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https://www.mathnet.ru/eng/faa27

https://doi.org/10.4213/faa27

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This publication is cited in the following 11 articles:

K. S. Shklyaev, “Plane sets that are Chebyshev in some norm”, Moscow University Mathematics Bulletin, 76:2 (2021), 69–72
A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$”, Math. Notes, 108:3 (2020), 309–317
A. R. Alimov, “Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 75:5 (2020), 209–215
A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730
A. R. Alimov, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454
A. R. Alimov, “Preservation of approximative properties of subsets of Chebyshev sets and suns in $\ell^\infty (n)$”, Izv. Math., 70:5 (2006), 857–866
A. R. Alimov, “Monotone path-connectedness of Chebyshev sets in the space $C(Q)$”, Sb. Math., 197:9 (2006), 1259–1272
A. R. Alimov, “Geometric construction of Chebyshev sets in the spaces $\ell^\infty(n)$, $c_0$ and $c$”, Russian Math. Surveys, 60:3 (2005), 559–561
A. R. Alimov, “Connectedness of suns in the space $c_0$”, Izv. Math., 69:4 (2005), 651–666
Alimov, AR, “Characterisations of Chebyshev sets in c(0)”, Journal of Approximation Theory, 129:2 (2004), 217

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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