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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
The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities
eBook ISBN:  978-1-4704-0214-3
Product Code:  MEMO/132/625.E
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $31.20
Add to cart
The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities
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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
eBook ISBN:  978-1-4704-0214-3
Product Code:  MEMO/132/625.E
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $31.20
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 132; 1998; 140 pp
    MSC: Primary 47; 49; 90

    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.

    Features:

    • 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.
    Readership

    Graduate students, research mathematicians, statisticians, operations researchers and economists working in functional analysis.
  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. The KKM principle related to Ky Fan minimax inequalities and fixed point theorems
    • 2. Equilibria of abstract economics in Hausdorff topological vector spaces
    • 3. Equilibria of abstract economics in locally convex topological vector spaces
    • 4. Equilibria in Frechet spaces
    • 5. Equilibria in topological spaces and some applications
    • 6. Maximal elements and coincidence theorems in product topological spaces
    • 7. Random abstract economics and applications
    • 8. Conclusion remarks
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 132; 1998; 140 pp
MSC: Primary 47; 49; 90

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.

Features:

  • 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.
Readership

Graduate students, research mathematicians, statisticians, operations researchers and economists working in functional analysis.
  • Chapters
  • Introduction
  • 1. The KKM principle related to Ky Fan minimax inequalities and fixed point theorems
  • 2. Equilibria of abstract economics in Hausdorff topological vector spaces
  • 3. Equilibria of abstract economics in locally convex topological vector spaces
  • 4. Equilibria in Frechet spaces
  • 5. Equilibria in topological spaces and some applications
  • 6. Maximal elements and coincidence theorems in product topological spaces
  • 7. Random abstract economics and applications
  • 8. Conclusion remarks
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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