Chebyshev centers and some geometric properties of Banach spaces

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• 作者：S. Lalithambigai^a ; ^{s_lalithambigai@yahoo.co.in} ; T. Paul^b ; ^{tanmoy@iith.ac.in} ; P. Shunmugaraj^c ; ^{psraj@iitk.ac.in} ; V. Thota^c ; ^{vamst@iitk.ac.in}
• 关键词：Chebyshev centers ; Kadec&ndash ; Klee property ; Set valued mappings ; Uniformly convex
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：926-938
• 全文大小：387 K
• 卷排序：449

文摘

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.