Introduction to Metric Spaces and Fixed Point T Theory

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.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