Fixed points, minimax inequalities and equilibria of noncompact abstract economies in \(FC\)-spaces. (English) Zbl 1157.47037

The authors first present a fixed point theorem in the setting of noncompact \(FC\)-spaces. Then they give several equivalent results to this fixed point theorem. As usual application of such kind of fixed point theorem, the authors derive a minimax theorem. Several maximal element theorems are also presented. Once again, as usual application of the maximal element theorems, several equilibrium existence results for abstract economies are derived.


47H10 Fixed-point theorems
49K35 Optimality conditions for minimax problems
91A10 Noncooperative games
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
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