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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Infimum Principle
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by Władysław Kulpa and Andrzej Szymanski PDF
Proc. Amer. Math. Soc. 132 (2004), 203-210 Request permission

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
  • Władysław 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
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 203-210
  • MSC (1991): Primary 52A07, 54H25, 90A56; Secondary 90D06
  • DOI: https://doi.org/10.1090/S0002-9939-03-06994-6
  • MathSciNet review: 2021263