Existence Theorems for Maximal Elements in H-Spaces with Applications on the Minimax Inequalities and Equilibrium of Games
Xian Wei Wu · Journal of Applied Analysis · 2000
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 [Fan, A minimax theorems and applications. Inequalities III, Academic Press, 1972, Tan and Yuan, J. Math. Econom. 23: 243–251, 1994, Yannelis and Prabhakar, J. Math. Econom. 12: 223–245, 1983, Yen, Pacific J. Math. 97: 477–481, 1981] to H -spaces, but also the open question raised by Yannelis and Prabhakar [J. Math. Econom. 12: 223–245, 1983] is answered in affirmative.