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Zusatztext "Clear! friendly exposition." (American Mathematical Monthly! August/September 2002) Informationen zum Autor 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. Klappentext 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 Zusammenfassung 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. Inhaltsverzeichnis Preface ix I Metric Spaces 1 Introduction 3 1.1 The real numbers R 3 1.2 Continuous mappings in R 5 1.3 The triangle inequality in R 7 1.4 The triangle inequality in R" 8 1.5 Brouwer's Fixed Point Theorem 10 Exercises 11 2 Metric Spaces 13 2.1 The metric topology 15 2.2 Examples of metric spaces 19 2.3 Completeness 26 2.4 Separability and connectedness 33 2.5 Metric convexity and convexity structures 35 Exercises 38 3 Metric Contraction Principles 41 3.1 Banach's Contraction Principle 41 3.2 Further extensions of Banach's Principle 46 3.3 The Caristi-Ekeland Principle 55 3.4 Equivalents of the Caristi-Ekeland Principle 58 3.5 Set-valued contractions 61 3.6 Generalized contractions 64 Exercises 67 4 Hyperconvex Spaces 71 4.1 Introduction 71 4.2 Hyperconvexity 77 4.3 Properties of hyperconvex spaces 80 4.4 A fixed point theorem 84 4.5 Intersections of hyperconvex spaces 87 4.6 Approximate fixed points 89 4.7 Isbell's hyperconvex hull 91 Exercises 98 5 "Normal" Structures in Metric Spaces 101<...
