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Advanced fixed point theory for econ...

McLennan, Andrew.

Advanced fixed point theory for economics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Advanced fixed point theory for economicsby Andrew McLennan.
Author:	McLennan, Andrew.
Published:	Singapore :Springer Singapore :2018.
Description:	xx, 432 p. :digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Fixed point theory.
Online resource:	http://dx.doi.org/10.1007/978-981-13-0710-2
ISBN:	9789811307102$q(electronic bk.)

Advanced fixed point theory for economics
McLennan, Andrew.

Advanced fixed point theory for economics[electronic resource] /by Andrew McLennan. - Singapore :Springer Singapore :2018. - xx, 432 p. :digital ;24 cm.

Chapter 1 Introduction and Summary -- Part I Topological Methods -- Chapter 2 Planes, Polyhedra, and Polytopes -- Chapter 3 Computing Fixed Points -- Chapter 4 Topologies on Spaces of Sets -- Chapter 5 Topologies on Functions and Correspondences -- Chapter 6 Metric Space Theory -- Chapter 7 Retracts -- Chapter 8 Essential Sets of Fixed Points -- Chapter 9 Approximation of Correspondences -- Part II Smooth Methods -- Chapter 10 Differentiable Manifolds -- Chapter 11 Sard's Theorem -- Chapter 12 Degree Theory -- Chapter 13 The Fixed Point Index -- Part III Applications and Extensions -- Chapter 14 Topological Consequences -- Chapter 15 Vector Fields and their Equilibria.

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.

ISBN: 9789811307102$q(electronic bk.)

Standard No.: 10.1007/978-981-13-0710-2doiSubjects--Topical Terms:

206244
Fixed point theory.

LC Class. No.: QA329.9 / .M354 2018

Dewey Class. No.: 515.7248

Advanced fixed point theory for economics
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245 1 0 $a Advanced fixed point theory for economics $h [electronic resource] / $c by Andrew McLennan.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2018.
300 $a xx, 432 p. : $b digital ; $c 24 cm.
505 0 $a Chapter 1 Introduction and Summary -- Part I Topological Methods -- Chapter 2 Planes, Polyhedra, and Polytopes -- Chapter 3 Computing Fixed Points -- Chapter 4 Topologies on Spaces of Sets -- Chapter 5 Topologies on Functions and Correspondences -- Chapter 6 Metric Space Theory -- Chapter 7 Retracts -- Chapter 8 Essential Sets of Fixed Points -- Chapter 9 Approximation of Correspondences -- Part II Smooth Methods -- Chapter 10 Differentiable Manifolds -- Chapter 11 Sard's Theorem -- Chapter 12 Degree Theory -- Chapter 13 The Fixed Point Index -- Part III Applications and Extensions -- Chapter 14 Topological Consequences -- Chapter 15 Vector Fields and their Equilibria.
520 $a 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.
650 0 $a Fixed point theory. $3 206244
650 0 $a Economics. $3 175999
650 2 4 $a Economic Theory/Quantitative Economics/Mathematical Methods. $3 731081
650 2 4 $a Game Theory, Economics, Social and Behav. Sciences. $3 274083
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-981-13-0710-2
950 $a Economics and Finance (Springer-41170)