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Zbl 0911.47055
Ding, Xieping
Fixed points, minimax inequalities and equilibria of noncompact abstract economies.
(English)
[J] Taiwanese J. Math. 2, No.1, 25-55 (1998). ISSN 1027-5487

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 ${\cal L}_F$ correspondences and ${\cal L}_F$-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 ${\cal L}_F$-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.
[J.Appell (Würzburg)]
MSC 2000:
*47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H04 Set-valued operators
91B50 Equilibrium in economics
47N10 Appl. of operator theory in optimization, math. programming, etc.
91A06 $n$-person games, $n>2$
91A13 Games with infinitely many players

Keywords: fixed point theorems; multivalued maps; minimax inequalities

Cited in: Zbl 1006.54041

Highlights
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