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

Part of: Nonlinear operators and their properties General convexity

Published online by Cambridge University Press:  09 April 2009

Mau-Hsiang Shih  and
Kok-Keong Tan
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

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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.

Keywords

minimax inequalityfixed pointinward and outward mapspartition of unityconvex settopological vector space.

MSC classification

Secondary: 52A07: Convex sets in topological vector spaces 47H10: Fixed-point theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 2 , October 1988 , pp. 169 - 183
Copyright
Copyright © Australian Mathematical Society 1988

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