In this paper, 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. (c) 2006 Elsevier Ltd. All rights reserved.
Bianchi, M., Kassay, G., Pini, R. (2007). Ekeland's principle for vector equilibrium problems. NONLINEAR ANALYSIS, 66(7), 1454-1464 [10.1016/j.na.2006.02.003].
Ekeland's principle for vector equilibrium problems
PINI, RITA
2007
Abstract
In this paper, 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. (c) 2006 Elsevier Ltd. All rights reserved.
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