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The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities
George Xian-Zhi Yuan, University of Queensland, Brisbane, Australia

Memoirs of the American Mathematical Society
1998; 140 pp; softcover
Volume: 132
ISBN-10: 0-8218-0747-1
ISBN-13: 978-0-8218-0747-7
List Price: US$49
Individual Members: US$29.40
Institutional Members: US$39.20
Order Code: MEMO/132/625
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This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.


  • Presents new results and recent development of KKM theory.
  • Offers an overview of modern and up-to-date treatment of the KKM theory, including related articles covering theory and applications.
  • Uses an interdisciplinary approach with specific applications in mathematics and economics.
  • Includes a comprehensive bibliography.


Graduate students, research mathematicians, statisticians, operations researchers and economists working in functional analysis.

Table of Contents

  • The KKM principle related to Ky Fan minimax inequalities and fixed point theorems
  • Equilibria of abstract economics in Hausdorff topological vector spaces
  • Equilibria of abstract economics in locally convex topological vector spaces
  • Equilibria in Frechet spaces
  • Equilibria in topological spaces and some applications
  • Maximal elements and coincidence theorems in product topological spaces
  • Random abstract economics and applications
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