Synopses & Reviews
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.
Review
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)
Review
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)
Table of Contents
Preface to the First Edition.- Preface to the Second Edition.- Introduction.- 1.Pre-requisites of fixed points.- 2.The Picard iteration.- 3.The Krasnoselskij iteration.- 4.The Mann iteration.- 5.The Ishikawa iteration.- 6.Other fixed point iteration procedures.- 7.Stability of fixed point iteration procedures.- 8.Iterative solution of nonlinear operator equations.- 9.Error analysis of fixed point iteration procedures.- References.- List of symbols.- Authors Index.- Subject Index.