Chebyshev centers and some geometric properties of Banach spaces

Lalithambigai, S and Paul, T and Shunmugaraj, P and Thota, V (2017) Chebyshev centers and some geometric properties of Banach spaces. Journal of Mathematical Analysis and Applications, 449 (1). pp. 926-938. ISSN 0022-247X

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Abstract

In this paper, we study two properties (P1)(P1) and (P2)(P2) introduced in the literature for studying the existence and stability of relative Chebyshev centers. We reformulate these properties in a way that leads naturally to our results. We mainly relate these properties with some geometric properties of Banach spaces. In particular, reflexive spaces having the Kadec-Klee property are characterized in terms of property (P1)(P1) and uniform convexity is characterized in terms of property (P2)(P2). Some continuity results for the center map are also presented.

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IITH Creators:
IITH CreatorsORCiD
Paul, Thttp://orcid.org/0000-0002-2043-3888
Item Type: Article
Uncontrolled Keywords: Chebyshev centers; Kadec-Klee property; Set valued mappings; Uniformly convex
Subjects: Mathematics
Depositing User: Team Library
Date Deposited: 22 Dec 2016 11:13
Last Modified: 10 Aug 2017 08:23
URI: http://raiith.iith.ac.in/id/eprint/2937
Publisher URL: httpS://doi.org/10.1016/j.jmaa.2016.12.026
OA policy: http://www.sherpa.ac.uk/romeo/issn/0022-247X/
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