Introduction to Metric Spaces and Fixed Point Theory (eBook)

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.

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.

"...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)