Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 61434, 5 pages
Review Article

Remarks of Equivalence among Picard, Mann, and Ishikawa Iterations in Normed Spaces

Xue Zhiqun

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

Received 1 April 2007; Revised 16 April 2007; Accepted 21 June 2007

Academic Editor: J. R. L. Webb

Copyright © 2007 Xue Zhiqun. 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.


We show that the convergence of Picard iteration is equivalent to the convergence of Mann iteration schemes for various Zamfirescu operators. Our result extends of Soltuz (2005).