Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 387056, 5 pages
Review Article

The Comparison of the Convergence Speed between Picard, Mann, Krasnoselskij and Ishikawa Iterations in Banach Spaces

Zhiqun Xue

Department of Mathematics and Physics, Shijiazhuang Railway Institute, Shijiazhuang 050043, China

Received 19 April 2007; Accepted 17 January 2008

Academic Editor: Brailey Sims

Copyright © 2008 Zhiqun Xue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this paper is to compare convergence speed of the Picard and Mann iterations on one hand, Krasnoselskij and Ishikawa iterations on the other hand, for the class of Zamfirescu operators. The results improve corresponding results of (Berinde 2004) and (Babu and Vara Prasad 2006).