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On New Generalized Viscosity Implicit Double Midpoint Rule for Hierarchical Problem

Author

Listed:
  • Thanyarat Jitpeera

    (Department of Science, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna (RMUTL), Chiangrai 57120, Thailand)

  • Anantachai Padcharoen

    (Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand)

  • Wiyada Kumam

    (Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computers Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand)

Abstract

The implicit midpoint rules are employed as a powerful numerical technique, and in this article we attend a class of viscosity iteration approximations on hierarchical problems for the implicit double midpoint rules. We prove the strong convergence theorem to the unique solution on hierarchical problem of this technique is established under some favorable conditions imposed on the control parameters in Hilbert spaces. Furthermore, we propose some applications to the constrained convex minimization problem, nonlinear Fredholm integral equation and variational inequality on fixed point problem. Moreover, some numerical examples are also presented to illustrate the different proposed methods and convergence results. Our results modified the implicit double midpoint rules with the hierarchical problem.

Suggested Citation

  • Thanyarat Jitpeera & Anantachai Padcharoen & Wiyada Kumam, 2022. "On New Generalized Viscosity Implicit Double Midpoint Rule for Hierarchical Problem," Mathematics, MDPI, vol. 10(24), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4755-:d:1003448
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    References listed on IDEAS

    as
    1. Poom Kumam & Thanyarat Jitpeera, 2014. "Strong Convergence of an Iterative Algorithm for Hierarchical Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, July.
    2. Lu-Chuan Ceng & Qamrul Hasan Ansari & Jen-Chih Yao, 2011. "Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 489-512, December.
    3. Yonghong Yao & Yeol Je Cho & Pei-Xia Yang, 2012. "An Iterative Algorithm for a Hierarchical Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, December.
    4. Gendai Gu & Shenghua Wang & Yeol Je Cho, 2011. "Strong Convergence Algorithms for Hierarchical Fixed Points Problems and Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-17, September.
    5. Giuseppe Marino & Hong-Kun Xu, 2011. "Explicit Hierarchical Fixed Point Approach to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 61-78, April.
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