An Introduction to Metric Spaces and Fixed Point Theory
Wiley Series in Pure and Applied Mathematics
1. Edition April 2001
320 Pages, Hardcover
Textbook
ISBN:
978-0-471-41825-2
John Wiley & Sons
Short Description
This book provides an excellent introduction to the subject designed for readers from a variety of mathematical backgrounds. It features introductory properties of metric spaces and Banach spaces, and an appendix contains a summary of the concepts of set theory.
Presents up-to-date Banach space results.
* Features an extensive bibliography for outside reading.
* Provides detailed exercises that elucidate more introductory material.
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.
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.
"...deserves to be on the bookshelf of everyone who wants to know about fixed-point theory in metric and Banach spaces and experts who want to read an insightful survey of some basic ideas..." (Mathematical Reviews, 2002b)
"Clear, friendly exposition." (American Mathematical Monthly, August/September 2002)
"Clear, friendly exposition." (American Mathematical Monthly, August/September 2002)
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, Tychonoff'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.
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.
