Advanced Fixed Point Theory for Economics

Beschreibung

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.

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 outstandingtext for advanced graduate courses in economics and related disciplines.

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

Autor*in

Andrew McLennan

Themen in »Advanced Fixed Point Theory for Economics«

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

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“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)

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