Elementary Fixed Point Theorems

• Main Author: Subrahmanyam, P.V (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Forum for Interdisciplinary Mathematics,
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Analysis.

This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky's theorem on periodic points, Thron's results on the convergence of certain real iterates, Shield's common fixe...

Table of Contents:

• Chapter 1. Prerequisites
• Chapter 2. Fixed Points of Some Real and Complex Functions
• Chapter 3. Fixed Points and Order
• Chapter 4. Partially Ordered Topological Spaces and Fixed Points
• Chapter 5. Contraction Principle
• Chapter 6. Applications of the Contraction Principle
• Chapter 7. Caristi's fixed point theorem
• Chapter 8. Contractive and Nonexpansive Mappings
• Chapter 9. Geometric Aspects of Banach Spaces and Nonexpansive Mappings
• Chapter 10. Brouwer's Fixed Point Theorem
• Chapter 11. Schauder's Fixed Point Theorem and Allied Theorems
• Chapter 12. Basic Analytic Degree Theory af a Mapping.