Chebyshev Centers that are Not Farthest Points

Debmalya Sain, Vladimir Kadets, Kallol Paul and Anubhab Ray ()
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Debmalya Sain: Saranagata, Dhandighi, Contai
Vladimir Kadets: Kharkiv V.N. Karazin National University
Kallol Paul: Jadavpur University
Anubhab Ray: Jadavpur University

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 2, 189-204

Abstract: Abstract In this paper, we address the question whether in a given Banach space, a Chebyshev center of a nonempty bounded subset can be a farthest point of the set. We obtain a characterization of two-dimensional real strictly convex spaces as those ones where a Chebyshev center cannot contribute to the set of farthest points of a subset. In dimension greater than two, every non-Hilbert smooth space contains a subset whose Chebyshev center is a farthest point. We explore the scenario in uniformly convex Banach spaces and further study the roles played by centerability and Mcompactness in the scheme of things to obtain a step by step characterization of strictly convex Banach spaces.

Keywords: Chebyshev center; farthest point; strict convexity; uniform convexity (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0262-y

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