Existence theorems for maximal elements in H-spaces with applications on the minimax inequalities and equilibrium of games

In this paper, we give two new existence theorems for maximal elements in H-spaces. As their applications, we obtain a extended version of Fan-Yen minimax inequality and some new existence theorems of an equilibrium for a qualitative game and an abstract economy. Our main results not only generalize the corresponding results of [4, 12, 15, 16] to H -spaces, but also the open question raised by Yannelis and Prabhakar [15] is answered in affirmative.