Two inertial projection-type methods for solving pseudo-monotone variational inequalities with application to image deblurring problem
Two inertial projection-type methods for solving pseudo-monotone variational inequalities with application to image deblurring problem
Our purpose is to propose two different type of inertial algorithms for approximating a solution of pseudo-monotone variational inequality problem in the framework of Banach spaces. The proposed algorithms are established by using Mann’s iterative method and single projection type method with adaptive step-size. Strong convergence theorems for minimum-norm solution of the variational inequality problem are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical experiments are performed to illustrate the advantage of the proposed methods and numerical experiments in image recovery are also presented. Our results generalize and improve some known results existing in the current literature.
Banach space, Minimum-norm, Pseudo-monotone mapping, Strong convergence, Variational inequality problem
Sunthrayuth, Pongsakorn
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Muangchoo, Kanikar
0710dfca-02e4-45f2-a514-1c5b82e6bcce
Jolaoso, Lateef Olakunle
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Oyewole, Olawale Kazeem
6e9e09ed-3aeb-4a42-acb3-67d7318288ec
1 February 2026
Sunthrayuth, Pongsakorn
3f5f8302-db73-41fa-9caf-5ed1782d41be
Muangchoo, Kanikar
0710dfca-02e4-45f2-a514-1c5b82e6bcce
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Oyewole, Olawale Kazeem
6e9e09ed-3aeb-4a42-acb3-67d7318288ec
Sunthrayuth, Pongsakorn, Muangchoo, Kanikar, Jolaoso, Lateef Olakunle and Oyewole, Olawale Kazeem
(2026)
Two inertial projection-type methods for solving pseudo-monotone variational inequalities with application to image deblurring problem.
Rendiconti del Circolo Matematico di Palermo Series 2, 75 (1), [10].
(doi:10.1007/s12215-025-01326-1).
Abstract
Our purpose is to propose two different type of inertial algorithms for approximating a solution of pseudo-monotone variational inequality problem in the framework of Banach spaces. The proposed algorithms are established by using Mann’s iterative method and single projection type method with adaptive step-size. Strong convergence theorems for minimum-norm solution of the variational inequality problem are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical experiments are performed to illustrate the advantage of the proposed methods and numerical experiments in image recovery are also presented. Our results generalize and improve some known results existing in the current literature.
Text
s12215-025-01326-1
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Accepted/In Press date: 5 August 2025
e-pub ahead of print date: 17 October 2025
Published date: 1 February 2026
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Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2025.
Keywords:
Banach space, Minimum-norm, Pseudo-monotone mapping, Strong convergence, Variational inequality problem
Identifiers
Local EPrints ID: 507306
URI: http://eprints.soton.ac.uk/id/eprint/507306
ISSN: 0009-725X
PURE UUID: c35934ed-9d1c-4c64-a907-a4d457a70286
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Date deposited: 03 Dec 2025 17:41
Last modified: 04 Dec 2025 02:58
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Contributors
Author:
Pongsakorn Sunthrayuth
Author:
Kanikar Muangchoo
Author:
Olawale Kazeem Oyewole
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