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Mat. Zametki, 1968, Volume 3, Issue 1, Pages 59–69 (Mi mz6652)  

This article is cited in 8 scientific papers (total in 8 papers)

Chebyshev sets and some generalizations of them

L. P. Vlasov

V. A. Steklov Institute of Mathematics, Sverdlovsk Branch of the Academy of Sciences of USSR

Abstract: In this note we generalize and strengthen certain results contained in [12]. For example, we establish that, in a uniformly convex and smooth Banach space, any locally compact Chebyshev set is convex

Full text: PDF file (850 kB)

English version:
Mathematical Notes, 1968, 3:1, 36–41

Bibliographic databases:

UDC: 517.5
Received: 07.08.1967

Citation: L. P. Vlasov, “Chebyshev sets and some generalizations of them”, Mat. Zametki, 3:1 (1968), 59–69; Math. Notes, 3:1 (1968), 36–41

Citation in format AMSBIB
\Bibitem{Vla68}
\by L.~P.~Vlasov
\paper Chebyshev sets and some generalizations of them
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 1
\pages 59--69
\mathnet{http://mi.mathnet.ru/mz6652}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=227745}
\zmath{https://zbmath.org/?q=an:0164.15004|0155.45401}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 1
\pages 36--41
\crossref{https://doi.org/10.1007/BF01386963}


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

    This publication is cited in the following articles:
    1. E. V. Oshman, “On the continuity of metric projection in Banach space”, Math. USSR-Sb., 9:2 (1969), 171–182  mathnet  crossref  zmath
    2. L. P. Vlasov, “Approximative properties of sets in normed linear spaces”, Russian Math. Surveys, 28:6 (1973), 1–66  mathnet  crossref  mathscinet  zmath
    3. E. N. Sosov, “On the continuity and connectedness of the metric $\delta$-projection in a uniformly convex geodesic space”, Russian Math. (Iz. VUZ), 45:3 (2001), 52–56  mathnet  mathscinet  zmath  elib
    4. Alimov, AR, “Characterisations of Chebyshev sets in c(0)”, Journal of Approximation Theory, 129:2 (2004), 217  crossref  isi
    5. A. R. Alimov, “Connectedness of suns in the space $c_0$”, Izv. Math., 69:4 (2005), 651–666  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. P. A. Borodin, “On the convexity of $N$-Chebyshev sets”, Izv. Math., 75:5 (2011), 889–914  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. 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  mathnet  crossref  mathscinet
    8. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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