Geometric properties, minimax inequalities, and fixed point theorems on convex spaces
Sehie Park, Jong Sook Bae, Hoo Kyung Kang · Proceedings of the American Mathematical Society · 1994
Using a selection theorem, we obtain a very general Ky Fan type geometric property of convex sets and apply it to the existence of maximizable quasiconcave functions, new minimax inequalities, and fixed point theorems for upper hemicontinuous multifunctions. Our results generalize works of Ha, Fan, Jiang, Himmelberg, and many others.