Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2010; 47(5): 1037-1040

Printed September 1, 2010

https://doi.org/10.4134/BKMS.2010.47.5.1037

Copyright © The Korean Mathematical Society.

A simple proof of the Sion minimax theorem

Sehie Park

Seoul National University

Abstract

For convex subsets $X$ of a topological vector space $E$, we show that a KKM principle implies a Fan-Browder type fixed point theorem and that this theorem implies generalized forms of the Sion minimax theorem.

Keywords: minimax theorem, KKM principle, Fan-Browder fixed point theorem

MSC numbers: 49B40, 49J35, 90C06, 90C30

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