On Generic Well-posedness of Restricted Chebyshev Center Problems in Banach Spaces

查看全文 作　　者：Chong [1]LI;Genaro [2]LOPEZ

机构地区：[1]Department of Mathematics,Zhejiang University;[2]Department of Mathematic Analysis,University of Sevilla

出　　处：《Acta Mathematica Sinica,English Series》索引2006年第22卷第3期,共10页

基　　金：supported in part by the National Natural Science Foundation of China(Grant No.10271025);supported in part by Projects BFM 2000-0344 and FQM-127 of Spain. 摘　　要：Let B(resp.K,Bl,Kl)denote the set of all nonempty bounded(resp.compact,bounded convex,compact convex)closed subsets of the Banach space X,endowed with the Hausdorffmetric,and let G be a nonempty relatively weakly compact closed subset of X.Let B° stand for theset of all F ∈ B such that the problem(F,G)is well-posed.We proved that,if X is strictly convex andKadec,the set Kl ∩ B° is a dense G_δ-subset of Kl\G.Furthermore,if X is a uniformly convexBanach space,we will prove more,namely that the set B\B°(resp.K\B°,Bl\B°,Kl\B°)is a-porous in B(resp.K,Bl,Kl).Moreover,we prove that for most(in the sense of the Bairecategory)closed bounded subsets G of X,the set K\B° is dense and uncountable in K. 关键词：Chebyshev中心点不确定轨迹非空界限 BANACH空间

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On Generic Well-posedness of Restricted Chebyshev Center Problems in Banach Spaces

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