Ekeland’s principle for vector equilibrium problems |
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| Authors: | M. Bianchi G. Kassay R. Pini |
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| Affiliation: | 1. Instituto di Econometria e Matematica per le Applicazioni Economiche, Finanziarie e Attuariali, Università Cattolica del Sacro Cuore di Milano, Largo Gemelli 1, 20123 Milano, Italy;2. Babes-Bolyai University Cluj, Faculty of Mathematics and Computer Science, Str. M. Kogalniceanu 1, 3400 Cluj, Romania;3. Dipartimento di Metodi Quantitativi per le Scienze Economiche e Aziendali, Università di Milano-Bicocca, Piazza dell’Ateneo Nuovo 1, 20126 Milano, Italy |
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| 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. |
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| Keywords: | Ekeland&rsquo s principle Vector equilibrium problem Quasi lower semicontinuity |
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