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© 2007

Iterative Approximation of Fixed Points

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1912)

Table of contents

About this book

Introduction

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, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration etc.), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented. Due to the explosive number of research papers on the topic (in the last 15 years only, more than one thousand articles related to the subject were published), it was felt that such a monograph was imperatively necessary. The volume is useful for authors, editors, and reviewers. It introduces concrete criteria for evaluating and judging the plethora of published papers.

Keywords

calculus convergence theorems equation fixed points iterative methods nonlinear contractive type operators rate of convergence theorem

Authors and affiliations

  1. 1.Department of Mathematics and Computer ScienceNorth University of Baia MareBaia MareRomania

Bibliographic information

  • Book Title Iterative Approximation of Fixed Points
  • Authors Vasile Berinde
  • Series Title Lecture Notes in Mathematics
  • DOI https://doi.org/10.1007/978-3-540-72234-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-540-72233-5
  • eBook ISBN 978-3-540-72234-2
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 2
  • Number of Pages XV, 326
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published by Editura Efemeride, Baia Mare, Romania, 2002
  • Topics Operator Theory
    Numerical Analysis
    Topology
  • Buy this book on publisher's site

Reviews

From the reviews of the second edition:

"This is a very thoroughly revised and enlarged version of the author’s previous monograph with the same title … . The book is a surprisingly pleasant reading, a very well done elaboration … . I suggest it to all departments of numerical analysis both for researchers, teachers and students. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations." (László L. Stachó, Acta Scientiarum Mathematicarum, Vol. 74, 2008)

"There is a huge amount of existence results for fixed points, very often from a purely theoretical viewpoint … . Specialists in the field will find the list of more than 1500 references particularly useful … this book may also serve as a guide to the literature." (Jürgen Appell, Zentralblatt MATH, Vol. 1165, 2009)