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ID：49297209
大小：947.16 KB
页数：38页
时间：2020-02-29
《局部凸空间一致凸性和连续函数可微性的研究.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、lrf$5eupS k-"R/_ j,Banachh9((qf<h9)n^WhUHy[~,DlA!qf<h9 C$Y&h9n^WA=B#.ÆY&h9n^W(,Y&h9,Ekeand kn,Asplund&^WBn?,=yfG-0.j56ijY&h9f ^WdHy[~.&>Banachh9Gateauxf Fr´echetf $Y&h9,z74k<,=yBF,&~k
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4、:(z7yBanachh9f%fx4k<ÆY&h9R.`hR:Y&h9;vWu;vWu;Gateauxf ;Fr´echetf ;4k5、LYSPACEABSTRACTInrecentdecades,thedevelopmentoftheoreticalstudyonBanachspace(ornormedlinearspace)hasbeendevelopingrapidly,onthecontrary,thetheoreticalstudyonlocallyconvexspaces,whichiswidelyspreadinBanachspace,developsslowly.ThescholarswhostudyontheDropproperty,Ekelandvariationalprinc6、iple,theAsplundpropertyandDifferentiationTheoryachievegreatsuccesses.Sincethebeginningofthiscentury,theresearchesoflocallyconvexspaceofdifferentiabilityHasalsobeenarapiddevelopment.Inthispaper,theauthormakesGateauxdifferentiabilityandFr´echetdifferentiabilityinBanachspaceintolocallyconvex7、space,givesnecessaryandsufficientconditionsaboutthemandmakesbetterResults.Thispaperisdividedintofourchapters:LetXbeareallinearspace,PafamilyofseparatedseminormsonX,(X,P)adual,(X,TP)alocallyconvexspacegeneratedbyP.Chapter1:Theknowledgeofpreparation.Chapter2:Thischaptergivesanecessaryands8、ufficientconditionofGateauxdif-ferentiabilityandFr´echetdifferentiabilityofcontinuousgaugefunctioninlocallyconvexspaces.Chapter3:Thischaptergivesanecessaryandsufficientconditionofcontinuousconvexfunctiondifferentiabilityinlocallyconvexspaces.Chapter4:Thischaptergivesasufficientconditionoftheu9、niformconvexityoflocallyconvexspacesinsteadofBanachspaces.KEYWORDS:locallyconvexspaces;continuousconvexfunction;continuousgaugefunction;Gateauxdifferentiability;Fr´echetdifferentiability;necessaryandsufficientconditionII{w.#.................................................................10、.....
5、LYSPACEABSTRACTInrecentdecades,thedevelopmentoftheoreticalstudyonBanachspace(ornormedlinearspace)hasbeendevelopingrapidly,onthecontrary,thetheoreticalstudyonlocallyconvexspaces,whichiswidelyspreadinBanachspace,developsslowly.ThescholarswhostudyontheDropproperty,Ekelandvariationalprinc
6、iple,theAsplundpropertyandDifferentiationTheoryachievegreatsuccesses.Sincethebeginningofthiscentury,theresearchesoflocallyconvexspaceofdifferentiabilityHasalsobeenarapiddevelopment.Inthispaper,theauthormakesGateauxdifferentiabilityandFr´echetdifferentiabilityinBanachspaceintolocallyconvex
7、space,givesnecessaryandsufficientconditionsaboutthemandmakesbetterResults.Thispaperisdividedintofourchapters:LetXbeareallinearspace,PafamilyofseparatedseminormsonX,(X,P)adual,(X,TP)alocallyconvexspacegeneratedbyP.Chapter1:Theknowledgeofpreparation.Chapter2:Thischaptergivesanecessaryands
8、ufficientconditionofGateauxdif-ferentiabilityandFr´echetdifferentiabilityofcontinuousgaugefunctioninlocallyconvexspaces.Chapter3:Thischaptergivesanecessaryandsufficientconditionofcontinuousconvexfunctiondifferentiabilityinlocallyconvexspaces.Chapter4:Thischaptergivesasufficientconditionoftheu
9、niformconvexityoflocallyconvexspacesinsteadofBanachspaces.KEYWORDS:locallyconvexspaces;continuousconvexfunction;continuousgaugefunction;Gateauxdifferentiability;Fr´echetdifferentiability;necessaryandsufficientconditionII{w.#.................................................................
10、.....
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