On Well-posed Mutually Nearest and Mutually Furthest Point Problems in Banach Spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On Well-posed Mutually Nearest and Mutually Furthest Point Problems in Banach Spaces

Authors:	Email author" target="_blank">Chong?Li Email author Ren?Xing?Ni

Institution:	(1) Department of Mathematics, Zhejiang University, Hangzhou, 310027, P. R. China;(2) Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, P. R. China;(3) Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, 312000, P. R. China

Abstract:	Abstract Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let ${\user1{K}}{\left( X \right)}$ denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let ${\user1{K}}_{G} {\left( X \right)}$ denote the closure of the set ${\left\{ {A \in {\user1{K}}{\left( X \right)}:A \cap G = \emptyset } \right\}}$ . We prove that the set of all $A \in {\user1{K}}_{G} {\left( X \right)}{\left( {{\text{resp}}{\text{.}}{\kern 1pt} A \in {\user1{K}}{\left( X \right)}} \right)}$ , such that the minimization (resp. maximization) problem min(A,G) (resp. max(A,G)) is well posed, contains a dense G _δ-subset of ${\user1{K}}_{G} {\left( X \right)}{\left( {{\text{resp}}{\text{.}}{\kern 1pt} {\kern 1pt} {\user1{K}}{\left( X \right)}} \right)}$ , thus extending the recent results due to Blasi, Myjak and Papini and Li. This work is partly supported by the National Natural Science Foundation of China (Grant No. 10271025)

Keywords:	Mutually nearest point Mutually furthest point Well posedness Dense G _δ -subset
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