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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, Volume 14, Issue 4(2), Pages 489–497 (Mi isu540)  

This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces

A. R. Alimov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, 1, Main Building, Leninskiye Gory, GSP-1, Moscow, 119991, Russia

Abstract: The well-known Tsar'kov's characterisation of finite-dimensional Banach spaces in which every bounded Chebyshev set (bounded $P$-acyclic set) is convex is extended to the asymmetrical setting.

Key words: bounded Chebyshev set, convexity, asymmetric norm.

DOI: https://doi.org/10.18500/1816-9791-2014-14-4-489-497

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Bibliographic databases:

UDC: 517.982.256

Citation: A. R. Alimov, “Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:4(2) (2014), 489–497

Citation in format AMSBIB
\Bibitem{Ali14}
\by A.~R.~Alimov
\paper Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 4(2)
\pages 489--497
\mathnet{http://mi.mathnet.ru/isu540}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-4-489-497}
\elib{http://elibrary.ru/item.asp?id=22625597}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. R. Alimov, E. V. Shchepin, “Convexity of Chebyshev sets with respect to tangent directions”, Russian Math. Surveys, 73:2 (2018), 366–368  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. R. Alimov, “Ogranichennaya styagivaemost strogikh solnts v trëkhmernykh prostranstvakh”, Fundament. i prikl. matem., 22:1 (2018), 3–11  mathnet  mathscinet
    3. S. I. Dudov, M. A. Osiptsev, “A Formula for the Superdifferential of the Distance Determined by the Gauge Function to the Complement of a Convex Set”, Math. Notes, 106:5 (2019), 703–710  mathnet  crossref  crossref  isi
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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