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Graph Convergence, Algorithms, and Approximation of Common Solutions of a System of Generalized Variational Inclusions and Fixed-Point Problems

Author

Listed:
  • 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)

  • Yu Zhang

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

  • Zhao-Li Ma

    (College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
    College of Public Foundation, Yunnan Open University, Kunming 650223, China)

Abstract

In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in the proximal mapping associated with a general H -monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. The main contribution of this work is the establishment of a new equivalence relationship between the graph convergence of a sequence of general strongly H -monotone mappings and their associated proximal mappings, respectively, to a given general strongly H -monotone mapping and its associated proximal mapping by using the notions of graph convergence and proximal mapping concerning a general strongly H -monotone mapping. By employing the concept of proximal mapping relating to general strongly H -monotone mapping, some iterative algorithms are proposed, and as an application of the obtained equivalence relationship mentioned above, a convergence theorem for approximating a common element of the set of solutions of a system of generalized variational inclusions involving general strongly H -monotone mappings and the set of fixed points of an ( { a n } , { b n } , ϕ ) -total uniformly L -Lipschitzian mapping is proved. It is significant to emphasize that our results are new and improve and generalize many known corresponding results.

Suggested Citation

  • Javad Balooee & Shih-Sen Chang & Lin Wang & Yu Zhang & Zhao-Li Ma, 2023. "Graph Convergence, Algorithms, and Approximation of Common Solutions of a System of Generalized Variational Inclusions and Fixed-Point Problems," Mathematics, MDPI, vol. 11(4), pages 1-29, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:832-:d:1059866
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    References listed on IDEAS

    as
    1. 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.
    2. R. U. Verma, 2006. "General System of A-Monotone Nonlinear Variational Inclusion Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 151-157, October.
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