Fixed points, minimax inequalities and equilibria of noncompact abstract economies

Several new fixed point theorems in H-space are first proved. Next, by appl ying the fixed point theorems, some minimax inequalities and existence theo rems of maximal elements for L-F correspondences and L-F-majorized correspo ndences 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 cor respondences 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, Tou ssaint, Tulcea, Yannelis and Yannelis-Prabhakar etc.