- Review Article
- Open Access
Remarks of Equivalence among Picard, Mann, and Ishikawa Iterations in Normed Spaces
© Xue Zhiqun. 2007
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).
- Şoltuz ŞM: The equivalence of Picard, Mann and Ishikawa iterations dealing with quasi-contractive operators. Mathematical Communications 2005,10(1):81–88.MATHMathSciNetGoogle Scholar
- Vasilev FP: Numerical Methods for Solving Extremal Problems. 2nd edition. Nauka, Moscow, Russia; 1988:550.Google Scholar
- Weng X: Fixed point iteration for local strictly pseudo-contractive mapping. Proceedings of the American Mathematical Society 1991,113(3):727–731. 10.1090/S0002-9939-1991-1086345-8MATHMathSciNetView ArticleGoogle Scholar
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.