In the literature, when dealing with equilibrium problems and the existence of their solutions, the most used assumptions are the convexity of the domain and the generalized convexity and monotonicity, together with some weak continuity assumptions, of the function. In this paper, we focus on conditions that do not involve any convexity concept, neither for the domain nor for the function involved. Starting from the well-known Ekeland's theorem for minimization problems, we find a suitable set of conditions on the function f that lead to an Ekeland's variational principle for equilibrium problems. Via the existence of c-solutions, we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems. (c) 2004 Elsevier Inc. All rights reserved.

Bianchi, M., Kassay, G., Pini, R. (2005). Existence of equilibria via Ekeland's principle. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 305(2), 502-512 [10.1016/j.jmaa.2004.11.042].

Existence of equilibria via Ekeland's principle

PINI, RITA
2005

Abstract

In the literature, when dealing with equilibrium problems and the existence of their solutions, the most used assumptions are the convexity of the domain and the generalized convexity and monotonicity, together with some weak continuity assumptions, of the function. In this paper, we focus on conditions that do not involve any convexity concept, neither for the domain nor for the function involved. Starting from the well-known Ekeland's theorem for minimization problems, we find a suitable set of conditions on the function f that lead to an Ekeland's variational principle for equilibrium problems. Via the existence of c-solutions, we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems. (c) 2004 Elsevier Inc. All rights reserved.
Articolo in rivista - Articolo scientifico
equilibrium problem; system of equilibrium problems; approximate solution; Ekeland's principle
English
15-mag-2005
305
2
502
512
none
Bianchi, M., Kassay, G., Pini, R. (2005). Existence of equilibria via Ekeland's principle. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 305(2), 502-512 [10.1016/j.jmaa.2004.11.042].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/1942
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