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Algorithmic Aspect and Convergence Analysis for System of Generalized Multivalued Variational-like Inequalities

Author

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  • Javad Balooee

    (School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran 1417935840, Iran)

  • Shih-Sen Chang

    (Center for General Education, China Medical University, Taichung 40402, Taiwan)

  • Lin Wang

    (College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China)

  • Zhaoli Ma

    (College of Public Foundation, Yunnan Open University, Kunming 650223, China)

Abstract

The main aim of this paper is twofold. Our first objective is to study a new system of generalized multivalued variational-like inequalities in Banach spaces and to establish its equivalence with a system of fixed point problems utilizing the concept of P - η -proximal mapping. The obtained alternative equivalent formulation is used and a new iterative algorithm for finding its approximate solution is suggested. Under some appropriate assumptions imposed on the mappings and parameters involved in the system of generalized multivalued variational-like inequalities, the existence of solution for the system mentioned above is proved and the convergence analysis of the sequences generated by our proposed iterative algorithm is discussed. The second objective of this work is to investigate and analyze the notion M - η -proximal mapping defined in the literature. Taking into account of the assumptions considered for such a mapping, we prove that every M - η -proximal mapping is actually P - η -proximal and is not a new one. At the same time, some comments relating to some existing results are pointed out.

Suggested Citation

  • Javad Balooee & Shih-Sen Chang & Lin Wang & Zhaoli Ma, 2022. "Algorithmic Aspect and Convergence Analysis for System of Generalized Multivalued Variational-like Inequalities," Mathematics, MDPI, vol. 10(12), pages 1-40, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2016-:d:836525
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    References listed on IDEAS

    as
    1. Jolaoso, Lateef O. & Shehu, Yekini & Yao, Jen-Chih, 2022. "Inertial extragradient type method for mixed variational inequalities without monotonicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 353-369.
    2. Qamrul Hasan Ansari & Javad Balooee, 2013. "Predictor–Corrector Methods for General Regularized Nonconvex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 473-488, November.
    3. Bing Tan & Xiaolong Qin & Jen-Chih Yao, 2022. "Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems," Journal of Global Optimization, Springer, vol. 82(3), pages 523-557, March.
    4. Javad Balooee, 2013. "Projection Method Approach for General Regularized Non-convex Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 192-209, October.
    5. Ram U. Verma, 2012. "General Class of Implicit Variational Inclusions and Graph Convergence on A-Maximal Relaxed Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 196-214, October.
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    Cited by:

    1. Árpád Bűrmen & Tadej Tuma, 2022. "Preface to the Special Issue on “Optimization Theory and Applications”," Mathematics, MDPI, vol. 10(24), pages 1-3, December.

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