J Austral Math Soc Ser A 45 pp169--183, 1988.

A Geometric Property of Convex Sets with Applications to Minimax Type Inequalities and Fixed Point Theorems

Mau-Hsiang Shih and Kok-Keong Tan

(Received 14 April 1986; revised 31 August 1986)

Abstract

A geometric property of convex sets which is equivalent to a minimax inequality of the Ky Fan type is formulated. This property is used directly to prove minimax inequalities of the von Neumann type, minimax inequalities of the Fan-Kneser type, and fixed point theorems for inward and outward maps.

1980 AMS Subject Classification: primary 52A07, 48A40; secondary 47H10

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Authors

Mau-Hsiang Shih: Department of Mathematics, Chung Yuan University, Chung-Li, Taiwan, Republic of China.
Kok-Keong Tan: Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada.

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