A Fixed-Point Farrago

• Main Author: Shapiro, Joel H. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Universitext,
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Numerical analysis.; Analysis.; Numerical Analysis.

This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophist...

Table of Contents:

• 1. From Newton to Google
• 2. Brouwer in Dimension Two
• 3. Contraction Mappings
• 4. Brouwer in Higher Dimensions
• 5. Nash Equilibrium
• 6. Nash's "one-page proof"
• 7. The Schauder Fixed-Point Theorem
• 8. The Invariant Subspace Problem
• 9. The Markov–Kakutani Theorem
• 10. The Meaning of Means
• 11. Paradoxical Decompositions
• 12. Fixed Points for Non-commuting Map Families
• 13. Beyond Markov–Kakutani
• A. Advanced Calculus
• B. Compact Metric Spaces
• C. Convex Sets and Normed Spaces
• D. Euclidean Isometries
• E. A Little Group Theory, a Little Set Theory
• References
• Index
• List of Symbols.