半非紧测度与集值am映象(英文)

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1、mappings,J.ofMath.Res.andExposition,4(1992),487-492.半非紧测度与集值AM映象孙　大　清(贵州大学数学系,贵阳550025)摘要本文以半非紧测度为工具研究一类非线性集值映象的性质,然后把所得结果用于证明微分包含的解的存在性.—170—©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.JournalofMathematicalResearch&ExpositionVol.1

2、7,No.2,165-170,May1997MeasuresofSemi-NoncompactnessandSet-ValuedXAM-MappingsSunDaqing(Dept.ofMath.,GuizhouUniversity,Guiyang550025)AbstractInthispaperwedefinemeasuresofsemi2noncompactnessinalocallyconvextopologicallinearspacewithrespecttoagivensemino

3、rm.Thenwegetafixedpointthe2oremforaclassofcondensingset2valuedmappingsandapplyittodifferentialinclu2sions.Keywordsorderedtopologicallinearspace,almostorder2boundedsetdifferentialinclu2sion.ClassificationAMS(1991)46A,47HöCCLO177.1Recently,manypapersar

4、econcernedwithexistencesoffixedpointsforset2valuedcontrac2tionmappings,see,e.g.,[9]andreferencetherein.Inthispaper,motivatiedbytheideasof[7].weintroduceanotionofmeasureofsemi2noncompactnessforsubsetsofatopologicalvectorlatticewhichnotonlyreducestotha

5、tgivenin[7]forthenormtopologyonaBanachlattice,butwhichappliesequallytotheweaktopologyinawideclassofBanachlattices.Theseideasleadnaturallytoconsideringaclassofset2valuedmappingswhichwecallset2valuedAM2mappingsandforwhichweproveafixedpointtheorem(Theor

6、em3).Let(E,S)bearealandlocallyconvextopologicallinearspace.WeassumethatthereisanorderrelationFinE,whichmakesEavectorlattiec.Forx∈E.Let+-+-x=x∨0,x=(-x)∨0,ûxû=x+x,E+={x∈EûxE0}.WeassumethatthetopologySandthepartialorderFsatisfythefollowingcondition(H):(

7、H)Letx∈E.If{xn}

8、hatthepositiveconeE+isS2closedinE.WeremarkthatifEisaBanachlatticeandifSisthenormtopologyonE,thencondition(H)isclearlysatis2fiedsincethelatticeoperationsarecontinuousforthenormtopology.IfSistheweaktopologyonaBanachlatticethenthesituationissomewhatdiff