FIXED POINTS, MINIMAX INEQUALITIES AND EQUILIBRIA OF NONCOMPACT ABSTRACT ECONOMIES

Abstract

Several new fixed point theorems in H-space are first proved. 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. Our 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 etc.