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Strong Convergence of the Viscosity Approximation Process for the Split Common Fixed‐Point Problem of Quasi‐Nonexpansive Mappings

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  • Jing Zhao
  • Songnian He

Abstract

Very recently, Moudafi (2011) introduced an algorithm with weak convergence for the split common fixed‐point problem. In this paper, we will continue to consider the split common fixed‐point problem. We discuss the strong convergence of the viscosity approximation method for solving the split common fixed‐point problem for the class of quasi‐nonexpansive mappings in Hilbert spaces. Our results improve and extend the corresponding results announced by many others.

Suggested Citation

  • Jing Zhao & Songnian He, 2012. "Strong Convergence of the Viscosity Approximation Process for the Split Common Fixed‐Point Problem of Quasi‐Nonexpansive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:438023
    DOI: 10.1155/2012/438023
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    References listed on IDEAS

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    1. Yonghong Yao & Wu Jigang & Yeong-Cheng Liou, 2012. "Regularized Methods for the Split Feasibility Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Yonghong Yao & Wu Jigang & Yeong-Cheng Liou, 2012. "Regularized Methods for the Split Feasibility Problem," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, February.
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    Cited by:

    1. Shubo Cao, 2013. "The Split Common Fixed Point Problem for ϱ‐Strictly Pseudononspreading Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Prashant Patel & Rahul Shukla, 2024. "Viscosity Approximation for Split Equality Generalized Mixed Equilibrium Problems With Semigroups of Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2024(1).

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