Ekelands variational principle and some related issues

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Ekelands variational principle and some related issues

VIETNAM NATIONAL UNIVERSITY - HCMC UNIVERSITY’ OF SCIENCEDinh Ngoe QuyEKELAND’S VARIATIONAL PRINCIPLEAND SOME RELATED ISSUESPhD THESIS IN MATHEMATICSH

Ekelands variational principle and some related issues Hochiininh City - 2012VIETNAM NATIONAL UNIVERSITY - HCMCUNIVERSITY OF SCIENCEDinh Ngoc QuyEKELAND'S VARIATIONAL PRINCIPLEAND SOME RELATED ISSUESMajor:

Mathematical OptimizationCodes: 62 46 20 01Referee 1: Assoc. Prof. Dr. Nguyen Dinh PhilReferee 2: Assoc. Prof. Dr. Mai Due ThanhReferee 3: Dr. Nguyen Ekelands variational principle and some related issues

Ba TinIndependent Referee 1: Assoc. Prof. Dr. Truong Xuan Due HaIndependent Referee 2: Assoc. Prof. Dr. Nguyen Dinh HuySCIENTIFIC SUPERVISORProf. D.S

Ekelands variational principle and some related issues

c Phan Quoc KhanhHochiminh City - 2012ConfirmationI confirm that all the results of this t hesis come from my work under the supervision of Professor

VIETNAM NATIONAL UNIVERSITY - HCMC UNIVERSITY’ OF SCIENCEDinh Ngoe QuyEKELAND’S VARIATIONAL PRINCIPLEAND SOME RELATED ISSUESPhD THESIS IN MATHEMATICSH

Ekelands variational principle and some related issues 1. A generalized distance and enhanced Ekelandb variational principle for vector functions11Introduction22Weak T-functions and generalized lower sein

icontinuity of a function33Lower closed transitive relations and minimal elements51The EVP95rhe EVP for the case of range space being a normed space12 Ekelands variational principle and some related issues

6Equivalent formulations13

VIETNAM NATIONAL UNIVERSITY - HCMC UNIVERSITY’ OF SCIENCEDinh Ngoe QuyEKELAND’S VARIATIONAL PRINCIPLEAND SOME RELATED ISSUESPhD THESIS IN MATHEMATICSH