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On minimax inequalities on spaces having certain contractible subsets

Published online by Cambridge University Press:  17 April 2009

Sehie Park
Sehie Park
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea The Mathematical Sciences Research, Institute of Korea, Seoul 151–742, Korea
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Abstract

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The concept of a convex space is extended to an H-space; that is, a space having certain family of contractible subsets. For such spaces the KKM type theorems, the Fan-Browder fixed point theorem, the Ky Fan type matching theorem, and minimax inequalities are given. Moreover, applications to a von Neumann-Sion type minimax theorem, a saddle point theorem, a quasi-variational inequality, and a Kakutani type fixed point theorem are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 1 , February 1993 , pp. 25 - 40
Copyright
Copyright © Australian Mathematical Society 1993

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