Chebyshev Centers that are Not Farthest Points |
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Authors: | Debmalya Sain Vladimir Kadets Kallol Paul Anubhab Ray |
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Institution: | 1.Saranagata, Dhandighi, Contai,Purba Medinipur,India;2.Department of Mathematics and Informatics,Kharkiv V.N. Karazin National University,Kharkiv,Ukraine;3.Department of Mathematics,Jadavpur University,Kolkata,India |
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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. |
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