Armenian Journal of Mathematics, 13(3)
2021; 1–20
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Viscosity approximation method for solving variational inequality problem in real Banach spaces

Godwin Ugwunnadi*

Received: 2024-12-07 · Published: 2021-07-15

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CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Viscosity approximation method for solving variational inequality problem in real Banach spaces
Author
Godwin Ugwunnadi
Source journal
Armenian Journal of Mathematics, 13(3)
Published
2021-07-15
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2021.13.3-1-20

Abstract

In this paper, we study the implicit and inertial-type viscosity approximation method for approximating a solution to the hierarchical variational inequality problem. Under some mild conditions on the parameters, we prove that the sequence generated by the proposed methods converges strongly to a solution of the above-mentioned problem in qq-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.
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