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Iterative Methods for Finding Solutions of a Class of Split Feasibility Problems over Fixed Point Sets in Hilbert Spaces

Author

Listed:
  • Suthep Suantai

    (Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Narin Petrot

    (Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
    Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand)

  • Montira Suwannaprapa

    (Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna, Chiang Rai 57120, Thailand)

Abstract

We consider the split feasibility problem in Hilbert spaces when the hard constraint is common solutions of zeros of the sum of monotone operators and fixed point sets of a finite family of nonexpansive mappings, while the soft constraint is the inverse image of a fixed point set of a nonexpansive mapping. We introduce iterative algorithms for the weak and strong convergence theorems of the constructed sequences. Some numerical experiments of the introduced algorithm are also discussed.

Suggested Citation

  • Suthep Suantai & Narin Petrot & Montira Suwannaprapa, 2019. "Iterative Methods for Finding Solutions of a Class of Split Feasibility Problems over Fixed Point Sets in Hilbert Spaces," Mathematics, MDPI, vol. 7(11), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1012-:d:280044
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    References listed on IDEAS

    as
    1. Hong-Kun Xu, 2011. "Averaged Mappings and the Gradient-Projection Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 360-378, August.
    2. Oganeditse Aaron Boikanyo, 2016. "The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-10, March.
    3. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
    4. 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, Hindawi, vol. 2012, pages 1-12, March.
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