An Introduction to Metric Spaces and Fixed Point Theory

A comprehensive, basic level introduction to metric spaces and fixed point theory
An Introduction to Metric Spaces and Fixed Point Theory presents a highly self–contained treatment of the subject that is accessible for students and researchers from diverse mathematical backgrounds, including those who may have had little training in mathematics beyond calculus. It provides up–to–date coverage of the properties of metric spaces and Banach spaces, as well as a detailed summary of the primary concepts of set theory.
The authors take a unique approach to the subject by including a number of helpful basic level exercises and using a simple and accessible level of presentation. They provide a highly comprehensive development of what is known in a purely metric context–especially in hyperconvex spaces–and a number of up–to–date Banach space results which are too recent to be found in other books on the subject.
In addition to introductory coverage of metric spaces and Banach spaces, the authors provide detailed analyses of these important topics in the subject:
∗ Metric contraction principles
∗ Hyperconvex spaces
∗ "Normal" structures in metric spaces
∗ Continuous mappings in Banach spaces
∗ Metric fixed point theory
∗ Banach space ultrapowers

Spis treści:
Preface.
METRIC SPACES.
Introduction.
Metric Spaces.
Metric Contraction Principles.
Hyperconvex Spaces.
"Normal" Structures in Metric Spaces.
BANACH SPACES.
Banach Spaces: Introduction.
Continuous Mappings in Banach Spaces.
Metric Fixed Point Theory.
Banach Space Ultrapowers.
Appendix: Set Theory.
Bibliography.
Index.

Nota biograficzna:
An Introduction to Metric Spaces and Fixed Point Theory includes an extensive bibliography and an appendix which provides a complete summary of the concepts of set theory, including Zorn′s Lemma, Ty chonoff′s Theorem, Zermelo′s Theorem, and transfinite induction. Detailed coverage of the newest developments in metric spaces and fixed point theory makes this the most modern and complete introduction to the subject available.
MOHAMED A. KHAMSI, PhD, is Professor in the Department of Mathematical Sciences at the University of Texas at El Paso and visiting Professor in the Department of Mathematics at Kuwait University. He is also co–author of Nonstandard Methods in Fixed Point Theory.
WILLIAM A. KIRK, PhD, is Professor in the Department of Mathematics at the University of Iowa, Iowa City, Iowa. He has authored over 100 journal articles and is co–author of Topics in Metric Fixed Point.

Okładka tylna:
A comprehensive, basic level introduction to metric spaces and fixed point theory
An Introduction to Metric Spaces and Fixed Point Theory presents a highly self–contained treatment of the subject that is accessible for students and researchers from diverse mathematical backgrounds, including those who may have had little training in mathematics beyond calculus. It provides up–to–date coverage of the properties of metric spaces and Banach spaces, as well as a detailed summary of the primary concepts of set theory.
The authors take a unique approach to the subject by including a number of helpful basic level exercises and using a simple and accessible level of presentation. They provide a highly comprehensive development of what is known in a purely metric context–especially in hyperconvex spaces–and a number of up–to–date Banach space results which are too recent to be found in other books on the subject.
In addition to introductory coverage of metric spaces and Banach spaces, the authors provide detailed analyses of these important topics in the subject:
∗ Metric contraction principles
∗ Hyperconvex spaces
∗ "Normal" structures in metric sp aces
∗ Continuous mappings in Banach spaces
∗ Metric fixed point theory
∗ Banach space ultrapowers