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

Fixed Point Theory and Applications volume 2006, Article number: 35704 (2007) Cite this article

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 and Affiliations

  1. Department of Mathematics, Andhra University, Visakhapatnam, 530 003, India

    GVR Babu

  2. Department of Mathematics, Dr. L. Bullayya College, Visakhapatnam, 530 013, India

    KNVV Vara Prasad

Authors
  1. GVR Babu
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  2. KNVV Vara Prasad
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Correspondence to GVR Babu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Babu, G., Vara Prasad, K. Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces. Fixed Point Theory Appl 2006, 35704 (2007). https://doi.org/10.1155/FPTA/2006/35704

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