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Common Fixed Point Iterations of Non-Lipschitzian Mappings in a Convex Metric Space

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Abstract

We establish strong convergence of the modified Moudafi iterative scheme to a common fixed point of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi-nonexpansive type mapping on a uniformly convex metric space. Our results either improve or generalize the corresponding results of Kim (Arab J Math 2:279–286, 2013), Kim and Kim (Comput Math Appl 42:1565–1570, 2001) and Rhoades (J Math Anal Appl 183:118–120, 1994).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Hafiz Fukhar-ud-din & Abdul Rahim Khan

  2. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    Hafiz Fukhar-ud-din

  3. Faculty of Mathematics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto

  4. Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Juan J. Nieto

Authors
  1. Hafiz Fukhar-ud-din
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  2. Juan J. Nieto
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  3. Abdul Rahim Khan
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Correspondence to Abdul Rahim Khan.

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Fukhar-ud-din, H., Nieto, J.J. & Khan, A.R. Common Fixed Point Iterations of Non-Lipschitzian Mappings in a Convex Metric Space. Mediterr. J. Math. 13, 2061–2071 (2016). https://doi.org/10.1007/s00009-015-0619-y

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  • DOI: https://doi.org/10.1007/s00009-015-0619-y

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