A Fixed-Point Farrago

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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Shapiro, Joel H. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edición:1st ed. 2016.
Colección:Universitext,
Temas:
Mathematical analysis.
Numerical analysis.
Analysis.
Numerical Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

Ejemplares similares