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Zbl 1157.47037
Ding, Xie Ping; Wang, Lei
Fixed points, minimax inequalities and equilibria of noncompact abstract economies in $FC$-spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl. 69, No. 2, A, 730-746 (2008). ISSN 0362-546X

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.
[Qamrul Hasan Ansari (Aligarh)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
49K35 Minimax problems (necessity and sufficiency)
91A10 Noncooperative games
47N10 Appl. of operator theory in optimization, math. programming, etc.

Keywords: fixed points; minimax inequalities; maximal elements; abstract economies; $FC$-spaces

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