Skip to main content
  • Book
  • © 2007

Iterative Approximation of Fixed Points

Authors:

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

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (9 chapters)

  1. Front Matter

    Pages I-XVII
  2. The Picard Iteration

    Pages 31-62
  3. The Mann Iteration

    Pages 89-112
  4. The Ishikawa Iteration

    Pages 113-134
  5. Back Matter

    Pages 221-322

About this book

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

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)

Authors and Affiliations

  • Department of Mathematics and Computer Science, North University of Baia Mare, Baia Mare, Romania

    Vasile Berinde

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

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2007

  • Softcover ISBN: 978-3-540-72233-5Published: 16 May 2007

  • eBook ISBN: 978-3-540-72234-2Published: 20 April 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 2

  • Number of Pages: XV, 326

  • Additional Information: Originally published by Editura Efemeride, Baia Mare, Romania, 2002

  • Topics: Operator Theory, Numerical Analysis, Topology

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions