Iterative Approximation of Fixed Points
The aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting,
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Vasile Berinde
Iterative Approximation of Fixed Points
1912
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1912
Vasile Berinde
Iterative Approximation of Fixed Points
ABC
Author Vasile Berinde Department of Mathematics and Computer Science Faculty of Sciences North University of Baia Mare Victoriei Nr. 76 430122 Baia Mare, Romania e-mail: [email protected] [email protected]
Library of Congress Control Number: 2007925692 Mathematics Subject Classification (2000): 47H10, 47J25, 47H09, 65J15, 54H25
2nd rev. and enlarged edition Originally (1st edition) published by Editura Efemeride, Baia Mare, Romania, 2002 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-72233-5 Springer Berlin Heidelberg New York ISBN-13 978-3-540-72233-5 Springer Berlin Heidelberg New York DOI 10.1007/978-3-540-72234-2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the author and SPi using a Springer LATEX package Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper
SPIN: 12057177
41/SPi
543210
To my parents
Preface to the Second Edition
This is a revised and enlarged version of the second printing (with up-dated bibliography, 2004) of the first edition, published by Efemeride in 2002. All chapters of the book were practically revised in a certain extent and some new Sections were also added with the aim to improve the coverage of the topic and to attain its main aim: to summarize in a gradual and natural way the most significant contributions to the approximation of fixed points of nonlinear contractive type mappings, by presenting, for each important iterative method, some of the most relevant, interesting and actual results. Only constructive fixed point theorems are mainly the subject of the book. A constructive fixed point theorem establishes not only the existence (and possibly, uniqueness) of the fixed points, but also provides a method for approximating these fixed points and, moreover, offers information on the data dependence of the fixed points (or, alternatively, on the stability of the fixed point iterative me
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