On the existence and approximation of solutions of generalized equilibrium problem on Hadamard manifolds
On the existence and approximation of solutions of generalized equilibrium problem on Hadamard manifolds
In this paper, we study the existence of solution of the generalized equilibrium problem (GEP) in the framework of an Hadamard manifold. Using the KKM lemma, we prove the existence of solution of the GEP and give the properties of the resolvent function associated with the problem under consideration. Furthermore, we introduce an iterative algorithm for approximating a common solution of the GEP and a fixed point problem. Using the proposed method, we obtain and prove a strong convergence theorem for approximating a solution of the GEP, which is also a fixed point of a nonexpansive mapping under some mild conditions. We give an application of our convergence result to a solution of the convex minimization problem. To illustrate the convergence of the method, we report some numerical experiments. The result in this paper extends the study of the GEP from the linear settings to the Hadamard manifolds.
Equilibrium problem, Extragradient method, Hadamard manifold, Pseudomonotone, Riemannian manifold
Oyewole, O.K.
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Jolaoso, L.O.
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Aremu, K.O.
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Aphane, M.
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Oyewole, O.K.
887b9e09-a4a3-4df9-9572-c2d19f1a6118
Jolaoso, L.O.
102467df-eae0-4692-8668-7f73e8e02546
Aremu, K.O.
7c8766e4-ec45-4093-baca-e79f01088056
Aphane, M.
dffa9fec-78a2-44d4-960f-26395b2a3555
Oyewole, O.K., Jolaoso, L.O., Aremu, K.O. and Aphane, M.
(2022)
On the existence and approximation of solutions of generalized equilibrium problem on Hadamard manifolds.
Journal of Inequalities and Applications, 2022 (1), [142].
(doi:10.1186/s13660-022-02883-0).
Abstract
In this paper, we study the existence of solution of the generalized equilibrium problem (GEP) in the framework of an Hadamard manifold. Using the KKM lemma, we prove the existence of solution of the GEP and give the properties of the resolvent function associated with the problem under consideration. Furthermore, we introduce an iterative algorithm for approximating a common solution of the GEP and a fixed point problem. Using the proposed method, we obtain and prove a strong convergence theorem for approximating a solution of the GEP, which is also a fixed point of a nonexpansive mapping under some mild conditions. We give an application of our convergence result to a solution of the convex minimization problem. To illustrate the convergence of the method, we report some numerical experiments. The result in this paper extends the study of the GEP from the linear settings to the Hadamard manifolds.
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s13660-022-02883-0
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Accepted/In Press date: 7 November 2022
e-pub ahead of print date: 15 November 2022
Keywords:
Equilibrium problem, Extragradient method, Hadamard manifold, Pseudomonotone, Riemannian manifold
Identifiers
Local EPrints ID: 475944
URI: http://eprints.soton.ac.uk/id/eprint/475944
ISSN: 1025-5834
PURE UUID: d2352836-a221-4798-ae1b-01188d7b7a6b
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Date deposited: 31 Mar 2023 16:44
Last modified: 18 Mar 2024 04:04
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Author:
O.K. Oyewole
Author:
K.O. Aremu
Author:
M. Aphane
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