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Zbl 1179.47047
Lin, Lai-Jiu; Chuang, Chih-Sheng; Al-Homidan, Suliman
Ekeland type variational principle with applications to quasi-variational inclusion problems. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, A, 651-661 (2010). ISSN 0362-546X

Summary: We study the Ekeland type variational principle, a Caristi-Kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces. By using these results, we establish some existence results for solutions of quasi-variational inclusion problems, quasi-optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces.

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47J22
47N10 Appl. of operator theory in optimization, math. programming, etc.
49J40 Variational methods including variational inequalities

Keywords: Ekeland type variational principle; Caristi-Kirk type fixed point theorem; quasi-variational inclusion problems; quasi-equilibrium problems; quasi-optimization problems; uniformly spaces; lower semicontinuity; sequentially lower monotone maps

Cited in: Zbl 1222.49021

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