Geometric properties, minimax inequalities, and fixed point theorems on convex spaces

Park, Sehie; Bae, Jong Sook; Kang, Hoo Kyung

doi:10.1090/S0002-9939-1994-1231303-6

Geometric properties, minimax inequalities, and fixed point theorems on convex spaces
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by Sehie Park, Jong Sook Bae and Hoo Kyung Kang

Proc. Amer. Math. Soc. 121 (1994), 429-439

DOI: https://doi.org/10.1090/S0002-9939-1994-1231303-6

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Abstract:

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.

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