Iterative Approximation of Fixed Points

  • Vasile┬áBerinde

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

  • Vasile┬áBerinde
    • 1
  1. 1.Department of Mathematics and Computer ScienceNorth University of Baia MareBaia MareRomania

Bibliographic information

  • 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
  • Print ISBN 978-3-540-72233-5
  • Online ISBN 978-3-540-72234-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book