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

 

Infimum Principle


Authors: Wladyslaw Kulpa and Andrzej Szymanski
Journal: Proc. Amer. Math. Soc. 132 (2004), 203-210
MSC (1991): Primary 52A07, 54H25, 90A56; Secondary 90D06
Published electronically: May 28, 2003
MathSciNet review: 2021263
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Abstract: We utilize the technique of dual sets to prove a theorem on the attainment of a simultaneous infimum by a compatible family of functions. Corollaries to the theorem include, among others, the von Neumann Minimax Principle and Nash's Equilibrium Theorem.


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Additional Information

Wladyslaw Kulpa
Affiliation: Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
Email: kulpa@ux2.math.us.edu.pl

Andrzej Szymanski
Affiliation: Department of Mathematics, Slippery Rock University, Slippery Rock, Pennsylvania 16057
Email: andrzej.szymanski@sru.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06994-6
PII: S 0002-9939(03)06994-6
Keywords: Simplicial space, dual family, fixed point
Received by editor(s): November 14, 2001
Received by editor(s) in revised form: August 14, 2002
Published electronically: May 28, 2003
Communicated by: Alan Dow
Article copyright: © Copyright 2003 American Mathematical Society