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Advanced Fixed Point Theory for Economics

  • Andrew McLennan

Table of contents

  1. Front Matter
    Pages i-xx
  2. Overview

    1. Front Matter
      Pages 1-1
    2. Andrew McLennan
      Pages 3-29
  3. Combinatoric Geometry

    1. Front Matter
      Pages 31-31
    2. Andrew McLennan
      Pages 33-54
    3. Andrew McLennan
      Pages 55-101
  4. Topological Methods

    1. Front Matter
      Pages 103-103
    2. Andrew McLennan
      Pages 105-116
    3. Andrew McLennan
      Pages 117-128
    4. Andrew McLennan
      Pages 129-142
    5. Andrew McLennan
      Pages 143-154
    6. Andrew McLennan
      Pages 155-172
    7. Andrew McLennan
      Pages 173-180
  5. Smooth Methods

    1. Front Matter
      Pages 181-181
    2. Andrew McLennan
      Pages 183-212
    3. Andrew McLennan
      Pages 213-225
    4. Andrew McLennan
      Pages 227-244
    5. Andrew McLennan
      Pages 245-265
  6. Applications

    1. Front Matter
      Pages 267-267
    2. Andrew McLennan
      Pages 269-288
    3. Andrew McLennan
      Pages 289-330
    4. Andrew McLennan
      Pages 331-370
    5. Andrew McLennan
      Pages 371-416
  7. Back Matter
    Pages 417-432

About this book

Introduction

This book develops the central aspect of fixed point theory – the topological fixed point index – to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems.

The book assumes the reader has no mathematical knowledge beyond that which is familiar to all theoretical economists. In addition to making the material available to a broad audience, avoiding algebraic topology results in more geometric and intuitive proofs.

Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well-written rigorous exposition of foundational mathematics. Numerous problems sketch key results from a wide variety of topics in theoretical economics, making the book an outstanding text for advanced graduate courses in economics and related disciplines.

Keywords

fixed point theory topology topological degree fixed point index economic modeling game theory mathematical economics economic theory topological methods metric space theory Nash equilibrium multivariate calculus Brouwer fixed point theorem Schauder fixed point theorem Lefschetz fixed point theorem Kakutani fixed point theorem Eilenberg–Montgomery theorem Fan–Glicksberg theorem general equilibrium theory differentiable manifold

Authors and affiliations

  • Andrew McLennan
    • 1
  1. 1.University of QueenslandSaint LuciaAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-13-0710-2
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Economics and Finance
  • Print ISBN 978-981-13-0709-6
  • Online ISBN 978-981-13-0710-2
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking