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Strong Convergence of a Modified Ishikawa Iterative Sequence for Asymptotically Quasi‐Pseudo‐Contractive‐Type Mappings

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  • Liuhong Li
  • Yuanheng Wang

Abstract

The purpose of this paper is to investigate the strong convergence problem of a modified mixed Ishikawa iterative sequence with errors for approximating the fixed points of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi‐pseudo‐contractive‐type mapping in an arbitrary real Banach space. The results here improve and extend the corresponding results reported by some other authors recently.

Suggested Citation

  • Liuhong Li & Yuanheng Wang, 2014. "Strong Convergence of a Modified Ishikawa Iterative Sequence for Asymptotically Quasi‐Pseudo‐Contractive‐Type Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:981494
    DOI: 10.1155/2014/981494
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    References listed on IDEAS

    as
    1. Dan Zhang & Xiaolong Qin & Feng Gu, 2012. "Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Lu-Chuan Ceng & Hong-Kun Xu & Ching-Feng Wen, 2013. "Relaxed Viscosity Approximation Methods with Regularization for Constrained Minimization Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Yonghong Yao & Rudong Chen & Giuseppe Marino & Yeong-Cheng Liou, 2012. "Applications of Fixed Point and Approximate Algorithms," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Yonghong Yao & Rudong Chen & Giuseppe Marino & Yeong-Cheng Liou, 2012. "Applications of Fixed Point and Approximate Algorithms," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-2, December.
    5. Dan Zhang & Xiaolong Qin & Feng Gu, 2012. "Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, February.
    6. Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Hybrid Method with Perturbation for Lipschitzian Pseudocontractions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Hybrid Method with Perturbation for Lipschitzian Pseudocontractions," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-20, July.
    8. Lu-Chuan Ceng & Ching-Feng Wen, 2013. "Composite Iterative Algorithms for Variational Inequality and Fixed Point Problems in Real Smooth and Uniformly Convex Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-21, July.
    9. Lu-Chuan Ceng & Hong-Kun Xu & Ching-Feng Wen, 2013. "Relaxed Viscosity Approximation Methods with Regularization for Constrained Minimization Problems," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-19, May.
    10. Lu-Chuan Ceng & Ching-Feng Wen, 2013. "Composite Iterative Algorithms for Variational Inequality and Fixed Point Problems in Real Smooth and Uniformly Convex Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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