Presents up-to-date Banach space results.
* Features an extensive bibliography for outside reading.
* Provides detailed exercises that elucidate more introductory material.
Diese Einführung in das Gebiet der metrischen Räume richtet sich in erster Linie nicht an Spezialisten, sondern an Anwender der Methode aus den verschiedensten Bereichen der Naturwissenschaften. Besonders ausführlich und anschaulich werden die Grundlagen von metrischen Räumen und Banach-Räumen erklärt, Anhänge enthalten Informationen zu verschiedenen Schlüsselkonzepten der Mengentheorie (Zornsches Lemma, Tychonov-Theorem, transfinite Induktion usw.). Die hinteren Kapitel des Buches beschäftigen sich mit fortgeschritteneren Themen.
Rezensionen / Stimmen
"...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)
Produkt-Info
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Maße
Höhe: 240 mm
Breite: 161 mm
Dicke: 22 mm
Gewicht
ISBN-13
978-0-471-41825-2 (9780471418252)
Schweitzer Klassifikation
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.
