Iterative approximation of fixed points

Bibliographic Information

Iterative approximation of fixed points

Vasile Berinde

(Lecture notes in mathematics, 1912)

Springer, c2007

2nd rev. and enl. ed

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Note

Originally published: Baia Mare, Romania : Editura Efemeride, 2002

Includes bibliographical references (p. [221]-304) and indexes

Description and Table of Contents

Description

This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.

Table of Contents

Pre-Requisites of Fixed Points.- The Picard Iteration.- The Krasnoselskij Iteration.- The Mann Iteration.- The Ishikawa Iteration.- Other Fixed Point Iteration Procedures.- Stability of Fixed Point Iteration Procedures.- Iterative Solution of Nonlinear Operator Equations.- Error Analysis of Fixed Point Iteration Procedures.

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