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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Geometric properties, minimax inequalities, and fixed point theorems on convex spaces


Authors: Sehie Park, Jong Sook Bae and Hoo Kyung Kang
Journal: Proc. Amer. Math. Soc. 121 (1994), 429-439
MSC: Primary 47H10; Secondary 46A99, 47H04, 47N10, 49J35
MathSciNet review: 1231303
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Abstract: Using a selection theorem, we obtain a very general Ky Fan type geometric property of convex sets and apply it to the existence of maximizable quasiconcave functions, new minimax inequalities, and fixed point theorems for upper hemicontinuous multifunctions. Our results generalize works of Ha, Fan, Jiang, Himmelberg, and many others.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1231303-6
PII: S 0002-9939(1994)1231303-6
Keywords: Convex space, polytope, compactly closed, multifunction, KKM theorem, Tietze extension theorem, Urysohn's lemma, selection, partition of unity, upper semicontinuous (u.s.c.), acyclic map, quasiconcave, minimax theorem, upper hemicontinuous (u.h.c.), inward set
Article copyright: © Copyright 1994 American Mathematical Society