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A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems

Published online by Cambridge University Press:  09 April 2009

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

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1988

References

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