广义Ekeland变分原理及其等价形式

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1、ᜧắᦻEkelandᑖᳮᐸắẆ：ᕜᢣ"ᦟ：$%ᦻᦟᣴ'()：*+,-ᑴᡠᙠ▾：ᦪ▾ᜧ20146ᨴ万方数据AThesisSubmittedtoChongqingNormalUniversityinPartialFulfillmentoftheRequirementsfortheDegreeofMasterGeneralizedEkeland’sVariationalPrincipleanditssomeequivalencesCandidate：ZhouL

2、iSupervisor：ProfessorPengJianwenMajor：OperationsResearchandCyberneticsCollege：CollegeofMathematicsScienceChongqingNormalUniversityJune2014万方数据ᜧắᦻ3ᦻ᤺⌕Ekelandᑖᳮᐸ᤺⌕Ekelandᑖᳮ（789:;“EVP”）ᙠ>?ឋᑖ᪆,ᨬCᓄ⚞FḄẆH3IJKᓝᑖ⌕ḄMᵨ。Pᦻ᪷RSᨵḄᦪUḄEkelandᑖᳮ，W⌕ᙠᦻX[16

3、,24,25]ḄYẠ[，ᙠᑖ]ᑡ_ᜓabcd[%eafgḄEVP，hᙠifgḄEVPḄYẠ[，jᑮgḄCaristi-Kirklmnopᳮq᩽ᜧᐗpᳮ；u᜜，wifgḄEVPḄឋxyẆH，jᑮᐸᙠapᩩ{8qCaristi-Kirklmnopᳮ！Oettli-Theralpᳮ、Takahashi᩽~ᓄpᳮ，hᑭᵨifgḄEVPwᙳ⊝⚪ḄḄᙠឋxyKẆH。Pᦻ᪷RSᨵḄᔣUḄEVP，W⌕ᙠᦻX[3,41,47,49]ḄYẠ[，ᙠ_ᜓcd[%eafgḄᔣUEVP，hᙠifgḄEVPḄYẠ[，jᑮgḄCa

4、risti-Kirklmnopᳮqaឋ，_ᗐhᦋxKᦻX[41]3Ḅa。，2.2⁚᪷RSᨵḄᦪUḄEVP，W⌕ᙠᦻX[16,24,25]ḄYẠ[，ᙠᑖ]ᑡ_ᜓabcd[%eafgḄEVP;2.3⁚，ᙠifgḄEVPḄYẠ[，jᑮgḄCaristi-Kirklmnopᳮq᩽ᜧᐗpᳮ；2.4⁚wifgḄEVPḄឋxyẆHjᑮᐸᙠapᩩ{8qCaristi-Kirklmnopᳮ、Oettli-Theralpᳮ、Takahashi᩽~ᓄpᳮ。，3.2⁚᪷RSᨵḄᔣUḄEVP，W⌕ᙠᦻX[3,41,47,

5、49]ḄYẠ[，ᙠ_ᜓcd[%eafgḄᔣUEVP;3.3⁚，ᙠifgḄEVPḄYẠ[，jᑮgḄCaristi-Kirklmnopᳮqaឋ，h_ᗐqᦋxKᦻX[41]3Ḅa。ᐵ：ᑖ]ᑡ_ᜓabcd;Caristi-Kirklmnopᳮ;Takahashi᩽~ᓄpᳮ;Ekelandᑖᳮ;_ᜓcd;Oettli-TheralpᳮI万方数据ᜧắᦻᦻ᤺⌕GeneralizedEkeland’sVariationalPrincipleanditssomeequivalencesABSTRACTIn

6、thispaper,wepresentageneralizedEkeland-typevariationalprincipleandaCaristi-Kirktypefixedpointtheoremandamaximalelementtheoreminthesettingofuniformspaces.WeprovesomeequivalencesofourvariationalprincipleswithCaristi-Kirktypefixedpointtheoremsformultivaluedmaps,th

7、eTakahashiminimizationtheoremandsomeotherrelatedresults.Asapplicationsofourresults,wederiveexistenceresultsforsolutionsofequilibriumproblemsandfixedpointtheoremsformultivaluedmaps.Thisgeneralizessomeexistingresultsforsequentiallylowermonotonemapsinamoregenerals

8、ettingandourtechniquesallowustoimproveandextendtheirresultsin[16,24,25].Furthermore,wepresentanequilibriumversionofvectorEkelandvariationalprinciple,andweprovesomeequivalenc