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Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications

Author

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  • Preeyanuch Chuasuk

    (Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand)

  • Anchalee Kaewcharoen

    (Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand)

Abstract

In this article, we discuss the hierarchical fixed point and split monotone variational inclusion problems and propose a new iterative method with the inertial terms involving a step size to avoid the difficulty of calculating the operator norm in real Hilbert spaces. A strong convergence theorem of the proposed method is established under some suitable control conditions. Furthermore, the proposed method is modified and used to derive a scheme for solving the split problems. Finally, we compare and demonstrate the efficiency and applicability of our schemes for numerical experiments as well as an example in the field of image restoration.

Suggested Citation

  • Preeyanuch Chuasuk & Anchalee Kaewcharoen, 2021. "Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications," Mathematics, MDPI, vol. 9(19), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2460-:d:649089
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    References listed on IDEAS

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    1. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
    2. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
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