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  • Review Article
  • Open Access

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

Fixed Point Theory and Applications20072007:061434

Received: 1 April 2007

Accepted: 21 June 2007

Published: 9 August 2007


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).


  • Differential Geometry
  • Normed Space
  • Computational Biology
  • Iteration Scheme
  • Picard Iteration


Authors’ Affiliations

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


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© Xue Zhiqun. 2007

This article is published under license to BioMed Central Ltd. 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.