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- W95838881 abstract "1. IntroductionLetDandAbetwononemptysubsetsinametricspace. Wesaythatthepair(D;A)satisflestheflx-flniteapproximationproperty(inshortF.F.A.P.)forafamilyFofmaps(ormultifunctions)fromD toA;ifforeveryf 2Fandall > 0thereexistsg 2Fwhichis-neartof andhasonlyaflnitenumberofflxedpoints. IntheparticularcasewhereD=A;wesaythatAsatisflestheF.F.A.P.forF:H. Hopf [4] proved by a special construction that any flnite polyhedronwhich is connected and which dimension is greater than one satisfles theF.F.A.P. for any continuous self-map. Later H. Schirmer [5] extended thisresulttoanycontinuousn-valuedmultifunction. AfterthisJ.B.BaillonandN.E.Rallisshowedin[1]thatanyflnite-unionofclosedconvexsubsetsofaBanachspacesatisflestheF.F.A.P.foranycompactself-map.In this paper we study the flx-flnite approximation property in normedvectorspaces.Weworkwiththepair(D;A)suchthatAsatisflestheSchaudercondition.IfxisapointofanormedspaceX andr>0;thenwedenotebyB(x;r)theopenballofradiusrandcenterx:AsubsetKofXissaidtoberelativelycompactifitsclosureKiscompact. Theconvexhullofasubsetfx" @default.
- W95838881 created "2016-06-24" @default.
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- W95838881 date "2002-01-01" @default.
- W95838881 modified "2023-09-28" @default.
- W95838881 title "Fix-Finite Approximation Property in Normed Vector Spaces" @default.
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