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

https://doi.org/10.1155/FPTA/2006/35704

Received: 25 April 2006

Accepted: 4 September 2006

Published: 25 January 2007

Abstract

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 .

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Authors’ Affiliations

(1)
Department of Mathematics, Andhra University
(2)
Department of Mathematics, Dr. L. Bullayya College

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Copyright

© 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.