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An Approximation Algorithm for the Combination of G -Variational Inequalities and Fixed Point Problems

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  • Araya Kheawborisut

    (Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

  • Atid Kangtunyakarn

    (Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

Abstract

In this paper, we introduce a modified form of the G -variational inequality problem, called the combination of G -variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element between the set of fixed points of a G -nonexpansive mapping and the solution set of the proposed G -variational inequality problem. Under appropriate assumptions, we establish a strong convergence theorem within the framework of a Hilbert space endowed with graphs. Additionally, we present the concept of the G -minimization problem, which diverges from the conventional minimization problem. Applying our main results, we demonstrate a strong convergence theorem for the G -minimization problem. Finally, we provide illustrative examples to validate and support our theoretical findings.

Suggested Citation

  • Araya Kheawborisut & Atid Kangtunyakarn, 2024. "An Approximation Algorithm for the Combination of G -Variational Inequalities and Fixed Point Problems," Mathematics, MDPI, vol. 13(1), pages 1-30, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:122-:d:1557687
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    References listed on IDEAS

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    1. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    2. Suthep Suantai & Mana Donganont & Watcharaporn Cholamjiak, 2019. "Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs," Mathematics, MDPI, vol. 7(10), pages 1-13, October.
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