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Systems of equilibrium problems with applications to new variants of Ekeland’s variational principle, fixed point theorems and parametric optimization problems. (English) Zbl 1218.49014
Summary: In this paper, we first establish some existence theorems of systems of generalized vector equilibrium problems. From these results, we obtain new variants of Ekeland’s variational principle in a Hausdorff topological vector space, a minimax theorem and minimization theorems. Some applications to the existence theorem of systems of semi-infinite problem, a variant of flower petal theorem and a generalization of Schauder’s fixed point theorem are also given.
MSC:
49J40Variational methods including variational inequalities
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47N10Applications of operator theory in optimization, convex analysis, programming, economics
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