Iterative Approximation of Fixed Points

Vasile Berinde (auth.)9783540722335, 3-540-72233-5

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.

Table of contents :
Front Matter….Pages I-XVII
Pre-Requisites of Fixed Points….Pages 3-30
The Picard Iteration….Pages 31-62
The Krasnoselskij Iteration….Pages 63-88
The Mann Iteration….Pages 89-112
The Ishikawa Iteration….Pages 113-134
Other Fixed Point Iteration Procedures….Pages 135-156
Stability of Fixed Point Iteration Procedures….Pages 157-178
Iterative Solution of Nonlinear Operator Equations….Pages 179-198
Error Analysis of Fixed Point Iteration Procedures….Pages 199-220
Back Matter….Pages 221-322