Overview
Provides comprehensive coverage of fixed point theory at the highest possible level of generality
Avoids use of algebraic topology, resulting in intuitive and geometric arguments as well as greater accessibility
Requires no mathematical knowledge beyond that which is common to all theoretical economists
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Table of contents (17 chapters)
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Front Matter
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Overview
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Front Matter
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Combinatoric Geometry
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Front Matter
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Smooth Methods
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Front Matter
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Applications
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Front Matter
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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
About this book
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.
Reviews
“The book realizes a remarkable synthesis, introducing the reader to the blend of economic insight, mathematical elegance and scientific impact. ‘Advance Fixed Point Theory for Economics’ is, in my opinion, an excellent book of mathematics for graduate students and researchers in theoretical economics and related disciplines.” (Mircea Balaj, zbMath 1418.91005, 2019)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Advanced Fixed Point Theory for Economics
Authors: Andrew McLennan
DOI: https://doi.org/10.1007/978-981-13-0710-2
Publisher: Springer Singapore
eBook Packages: Economics and Finance, Economics and Finance (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-13-0709-6Published: 20 July 2018
Softcover ISBN: 978-981-13-4485-5Published: 19 January 2019
eBook ISBN: 978-981-13-0710-2Published: 03 July 2018
Edition Number: 1
Number of Pages: XX, 432
Number of Illustrations: 18 b/w illustrations
Topics: Economic Theory/Quantitative Economics/Mathematical Methods, Game Theory, Economics, Social and Behav. Sciences