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A New Extragradient-Viscosity Method for a Variational Inequality, an Equilibrium Problem, and a Fixed Point Problem

Author

Listed:
  • Maryam Yazdi

    (Young Researchers and Elite Club, Malard Branch, Islamic Azad University, Malard MX7C+G74, Iran
    These authors contributed equally to this work.)

  • Saeed Hashemi Sababe

    (Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2R3, Canada
    These authors contributed equally to this work.)

Abstract

In this research article, we introduce a novel iterative approach that builds upon a two-step extragradient-viscosity method. This method aims to find a common element among the solution set of a variational inequality, an equilibrium problem, and the set of common fixed points from a countable family of demicontractive mappings in a Hilbert space. We offer a robust convergence theorem for the proposed iterative scheme, considering certain well-conditioned parameters. Our findings represent an improvement over similar results already available in the existing literature. Furthermore, we demonstrate the applicability of our main result to W-mappings. Lastly, we present two numerical examples to exhibit the consistency and accuracy of our devised scheme.

Suggested Citation

  • Maryam Yazdi & Saeed Hashemi Sababe, 2024. "A New Extragradient-Viscosity Method for a Variational Inequality, an Equilibrium Problem, and a Fixed Point Problem," Mathematics, MDPI, vol. 12(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3466-:d:1515393
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    References listed on IDEAS

    as
    1. Migot, Tangi & Cojocaru, Monica-G., 2020. "A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1136-1147.
    2. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
    3. N. Nadezhkina & W. Takahashi, 2006. "Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 191-201, January.
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