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
-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
-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.