Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503202 | Journal of Mathematical Analysis and Applications | 2005 | 11 Pages |
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 ε-solutions, we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Monica Bianchi, Gábor Kassay, Rita Pini,