On Generic Well-posedness of Restricted Chebyshev Center Problems in Banach Spaces-中国期刊网

摘要 LetB(resp.K,Bl,Kl)denotethesetofallnonemptybounded(resp.compact,boundedconvex,compactconvex)closedsubsetsoftheBanachspaceX,endowedwiththeHausdorffmetric,andletGbeanonemptyrelativelyweaklycompactclosedsubsetofX.LetB°standforthesetofallF∈Bsuchthattheproblem(F,G)iswell-posed.Weprovedthat,ifXisstrictlyconvexandKadec,thesetKl∩B°isadenseG_δ-subsetofKl\G.Furthermore,ifXisauniformlyconvexBanachspace,wewillprovemore,namelythatthesetB\B°(resp.K\B°,Bl\B°,Kl\B°)isa-porousinB(resp.K,Bl,Kl).Moreover,weprovethatformost(inthesenseoftheBairecategory)closedboundedsubsetsGofX,thesetK\B°isdenseanduncountableinK.

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

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

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