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Fixed points, minimax inequalities and equilibria of noncompact abstract economies. (English) Zbl 0911.47055
The author proves several fixed point theorems for multivalued maps in H-spaces. Next, by applying the fixed point theorems, some minimax inequalities and existence theorems of maximal elements for ${ℒ}_{F}$ correspondences and ${ℒ}_{F}$-majorized correspondences in H-spaces are obtained. Finally, using the existence theorems of maximal elements, some equilibrium existence theorems for one-person games, qualitative games and noncompact abstract economies with ${ℒ}_{F}$-majorized correspondences in H-spaces are obtained. These theorems improve and generalize most known results due to Border, Borglin-Keiding, Ding-Kim-Tan, Ding-Tan, Ding-Tarafdar, Mehta-Tarafdar, Shafer-Sonnenschein, Tan-Yuan, Tarafdar, Toussaint, Tulcea, Yannelis and Yannelis-Prabhakar, and others.

MSC:
 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47H04 Set-valued operators 91B50 General equilibrium theory in economics 47N10 Applications of operator theory in optimization, convex analysis, programming, economics 91A06 $n$-person games, $n>2$ 91A13 Games with infinitely many players