Advanced Fixed Point Theory for Economics

Andrew McLennan received his PhD from Princeton in 1982 under the supervision of Hugo Sonnenschein, and is currently Professor at the University of Queensland School of Economics. His primary research interests are in game theory, mathematical economics and microeconomics.

• 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.

“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)