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Zbl 1110.49007
Bianchi, M.; Kassay, G.; Pini, R.
Ekeland's principle for vector equilibrium problems. (English)
[J] Nonlinear Anal., Theory Methods Appl. 66, No. 7, A, 1454-1464 (2007). ISSN 0362-546X

Summary: The authors deal with bifunctions defined on complete metric spaces and with values in locally convex spaces ordered by closed convex cones. The aim is to provide a vector version of Ekeland's theorem related to equilibrium problems. To prove this principle, a weak notion of continuity of a vector-valued function is considered, and some of its properties are presented. Via the vector Ekeland's principle, existence results for vector equilibria are proved in both compact and noncompact domains.

MSC 2000:: *49J40 Variational methods including variational inequalities
49J53 Set-valued and variational analysis

Keywords: Ekeland's principle; vector equilibrium problem; quasi lower semicontinuity

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