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  • Research Article
  • Open Access

Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces

Fixed Point Theory and Applications20072006:35704

  • Received: 25 April 2006
  • Accepted: 4 September 2006
  • Published:


Let be an arbitrary real Banach space and a nonempty, closed, convex (not necessarily bounded) subset of . If is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant , then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of .


  • Banach Space
  • Differential Geometry
  • Computational Biology
  • Real Banach Space
  • Ishikawa Iteration


Authors’ Affiliations

Department of Mathematics, Andhra University, Visakhapatnam, 530 003, India
Department of Mathematics, Dr. L. Bullayya College, Visakhapatnam, 530 013, India


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© G. V. R. Babu and K. N. V. V. Vara Prasad. 2006

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.