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The Split Feasibility Problem with Multiple Output Sets for Demicontractive Mappings

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  • Fenghui Wang

    (Luoyang Normal University)

Abstract

In Hilbert spaces, we study the split feasibility problem with multiple output sets for demicontractive mappings. For solving this problem, we propose an iterative method and construct two selection strategies of stepsizes, namely the fixed stepsize and the variable stepsize. Under appropriate conditions, we prove the weak convergence of the proposed iterative method and the strong convergence of its variant. Furthermore, the experimental results show that the stepsize we constructed is very helpful to improve the convergence speed of the iterative method.

Suggested Citation

  • Fenghui Wang, 2022. "The Split Feasibility Problem with Multiple Output Sets for Demicontractive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 837-853, December.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:3:d:10.1007_s10957-022-02096-x
    DOI: 10.1007/s10957-022-02096-x
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    References listed on IDEAS

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    1. Yamin Wang & Fenghui Wang & Hong-Kun Xu, 2016. "Error Sensitivity for Strongly Convergent Modifications of the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 901-916, March.
    2. Andrzej Cegielski, 2015. "General Method for Solving the Split Common Fixed Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 385-404, May.
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