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Convergence to common fixed points by a modified iteration process

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Abstract

We modify an iteration process of Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61–79, 2007) to the case of two mappings and prove some weak and strong convergence theorems for two asymptotically nonexpansive mappings. We also point out that this process cannot be used for three mappings in its existing form even for nonexpansive mappings. We have to impose an extra condition to get convergence. We give an example to show that there do exist two nonexpansive mappings satisfying that condition.

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Author notes

  1. Safeer Hussain Khan

    Present address: Department of Mathematics, Statistics and Physics, Qatar University, Doha, 2713, Qatar

Authors and Affiliations

  1. Department of Mathematics Education, Gyeongsang National University, Chinju, South Korea

    Y. J. Cho

  2. Department of Mathematics, Lahore University of Management Sciences, 54792, Lahore, Pakistan

    Mujahid Abbas

Authors
  1. Safeer Hussain Khan
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  2. Y. J. Cho
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  3. Mujahid Abbas
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Correspondence to Safeer Hussain Khan.

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The first author thanks Qatar University for support in this work.

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Khan, S.H., Cho, Y.J. & Abbas, M. Convergence to common fixed points by a modified iteration process. J. Appl. Math. Comput. 35, 607–616 (2011). https://doi.org/10.1007/s12190-010-0381-z

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  • DOI: https://doi.org/10.1007/s12190-010-0381-z

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