The Ekeland variational principle for equilibrium problems revisited and applications. (June 2015)

• Record Type: Journal Article
• Authors: Alleche, Boualem; Rădulescu, Vicenţiu D.
• Is Part Of: Nonlinear analysis. Volume 23(2015)
• Page Start: 17
• Page End: 25
• Publication Date: 2015-06
• Subjects: Equilibrium problem -- System of equilibrium problems -- Quasi-hemivariational inequality -- Ekeland variational principle -- Multivalued mapping; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.11.006
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study the Ekeland variational principle for equilibrium problems under the setting of real Banach spaces. We make use of techniques related to infinite dimensional spaces to solve the weakly compact case and introduce a suitable weakened set of coerciveness to deal with the non weakly compact case. Some old results for the Euclidean space R n are generalized under weakened conditions of semicontinuity and applications to countable rather than finite systems of equilibrium problems on real Banach spaces are derived. Applications to quasi-hemivariational inequalities are discussed.