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Izvestiya: Mathematics, 2011, Volume 75, Issue 5, Pages 889–914
DOI: https://doi.org/10.1070/IM2011v075n05ABEH002557 (Mi im4280) 		 
This article is cited in 14 scientific papers (total in 14 papers)

On the convexity of $N$-Chebyshev sets

P. A. Borodin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (399 kB) Citations (14) Russian version article
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DOI: https://doi.org/10.1070/IM2011v075n05ABEH002557
Abstract: We define $N$-Chebyshev sets in a Banach space $X$ for every positive integer $N$ (when $N=1$, these are ordinary Chebyshev sets) and study conditions that guarantee their convexity. In particular, we prove that all $N$-Chebyshev sets are convex when $N$ is even and $X$ is uniformly convex or $N\geqslant 3$ is odd and $X$ is smooth uniformly convex.
Keywords: Chebyshev set, convexity problem.
Received: 29.12.2009
Revised: 03.06.2010
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
MSC: 46B20, 41A50, 41A65
Language: English
Original paper language: Russian
Citation: P. A. Borodin, “On the convexity of $N$-Chebyshev sets”, Izv. Math., 75:5 (2011), 889–914
Citation in format AMSBIB
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\by P.~A.~Borodin
\paper On the convexity of $N$-Chebyshev sets
\jour Izv. Math.
\yr 2011
\vol 75
\issue 5
\pages 889--914
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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