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Ekeland’s principle for vector equilibrium problems. (English) Zbl 1110.49007
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:
49J40Variational methods including variational inequalities
49J53Set-valued and variational analysis