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Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings

Author

Listed:
  • Prasit Cholamjiak

    (School of Science, University of Phayao, Phayao 56000, Thailand)

  • Suparat Kesornprom

    (School of Science, University of Phayao, Phayao 56000, Thailand)

  • Nattawut Pholasa

    (School of Science, University of Phayao, Phayao 56000, Thailand)

Abstract

In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main theorem.

Suggested Citation

  • Prasit Cholamjiak & Suparat Kesornprom & Nattawut Pholasa, 2019. "Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:167-:d:205644
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    References listed on IDEAS

    as
    1. Fenghui Wang & Huanhuan Cui, 2012. "On the contraction-proximal point algorithms with multi-parameters," Journal of Global Optimization, Springer, vol. 54(3), pages 485-491, November.
    2. Q. L. Dong & Y. J. Cho & L. L. Zhong & Th. M. Rassias, 2018. "Inertial projection and contraction algorithms for variational inequalities," Journal of Global Optimization, Springer, vol. 70(3), pages 687-704, March.
    3. S. Takahashi & W. Takahashi & M. Toyoda, 2010. "Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 27-41, October.
    4. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
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    Cited by:

    1. Raweerote Suparatulatorn & Anchalee Khemphet, 2019. "Tseng Type Methods for Inclusion and Fixed Point Problems with Applications," Mathematics, MDPI, vol. 7(12), pages 1-16, December.

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