Double inertial extrapolations method for solving split generalized equilibrium, fixed point and variational inequity problems

James Abah Ugboh; Joseph Oboyi; Hossam A. Nabwey; Christiana Friday Igiri; Francis Akutsah; Ojen Kumar Narain; James Abah Ugboh; Joseph Oboyi; Hossam A. Nabwey; Christiana Friday Igiri; Francis Akutsah; Ojen Kumar Narain

doi:10.3934/math.2024509

AIMS Mathematics

2024, Volume 9, Issue 4: 10416-10445. doi: 10.3934/math.2024509

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Double inertial extrapolations method for solving split generalized equilibrium, fixed point and variational inequity problems

1.
Department of Mathematics, University of Calabar, Calabar, Nigeria
2.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
3.
Department of Basic Engineering, Faculty of Engineering, Menoufia University, Shibin el Kom 32511, Egypt
4.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

Received: 24 December 2023 Revised: 23 February 2024 Accepted: 08 March 2024 Published: 15 March 2024
MSC : 26A33, 34B10, 34B15

This article proposes an iteration algorithm with double inertial extrapolation steps for approximating a common solution of split equilibrium problem, fixed point problem and variational inequity problem in the framework of Hilbert spaces. Unlike several existing methods, our algorithm is designed such that its implementation does not require the knowledge of the norm of the bounded linear operator and the value of the Lipschitz constant. The proposed algorithm does not depend on any line search rule. The method uses a self-adaptive step size which is allowed to increase from iteration to iteration. Furthermore, using some mild assumptions, we establish a strong convergence theorem for the proposed algorithm. Lastly, we present a numerical experiment to show the efficiency and the applicability of our proposed iterative method in comparison with some well-known methods in the literature. Our results unify, extend and generalize so many results in the literature from the setting of the solution set of one problem to the more general setting common solution set of three problems.
- double inertial technique,
- split generalized equilibrium,
- fixed point and variational inequity problems
Citation: James Abah Ugboh, Joseph Oboyi, Hossam A. Nabwey, Christiana Friday Igiri, Francis Akutsah, Ojen Kumar Narain. Double inertial extrapolations method for solving split generalized equilibrium, fixed point and variational inequity problems[J]. AIMS Mathematics, 2024, 9(4): 10416-10445. doi: 10.3934/math.2024509

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Abstract

This article proposes an iteration algorithm with double inertial extrapolation steps for approximating a common solution of split equilibrium problem, fixed point problem and variational inequity problem in the framework of Hilbert spaces. Unlike several existing methods, our algorithm is designed such that its implementation does not require the knowledge of the norm of the bounded linear operator and the value of the Lipschitz constant. The proposed algorithm does not depend on any line search rule. The method uses a self-adaptive step size which is allowed to increase from iteration to iteration. Furthermore, using some mild assumptions, we establish a strong convergence theorem for the proposed algorithm. Lastly, we present a numerical experiment to show the efficiency and the applicability of our proposed iterative method in comparison with some well-known methods in the literature. Our results unify, extend and generalize so many results in the literature from the setting of the solution set of one problem to the more general setting common solution set of three problems.

References

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