Fixed Point Theory in Distance Spaces

• Main Authors: Kirk, William (Author), Shahzad, Naseer (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Subjects: Mathematics.; Mathematical models.; Differential geometry.; Topology.; Differential Geometry.; Mathematical Modeling and Industrial Mathematics.

This is a monograph on fixed point theory, covering the purely metric aspects of the theory–particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This a...

Table of Contents:

• Preface
• Part 1. Metric Spaces
• Introduction
• Caristi’s Theorem and Extensions.- Nonexpansive Mappings and Zermelo’s Theorem
• Hyperconvex metric spaces
• Ultrametric spaces
• Part 2. Length Spaces and Geodesic Spaces
• Busemann spaces and hyperbolic spaces
• Length spaces and local contractions
• The G-spaces of Busemann
• CAT(0) Spaces
• Ptolemaic Spaces
• R-trees (metric trees)
• Part 3. Beyond Metric Spaces
• b-Metric Spaces
• Generalized Metric Spaces
• Partial Metric Spaces
• Diversities
• Bibliography
• Index.