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Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators

Fixed Point Theory and Applications volume 2004, Article number: 716359 (2004) Cite this article

Abstract

In the class of quasi-contractive operators satisfying Zamfirescu's conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent to the unique fixed point. In this paper, the comparison of the first two methods with respect to their convergence rate is obtained.

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  1. Department of Mathematics and Computer Science, North University of Baia Mare, Victorie 76, Baia Mare, 430072, Romania

    Vasile Berinde

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  1. Vasile Berinde
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Correspondence to Vasile Berinde.

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Berinde, V. Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators. Fixed Point Theory Appl 2004, 716359 (2004). https://doi.org/10.1155/S1687182004311058

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  • DOI: https://doi.org/10.1155/S1687182004311058