Viscosity extragradient with modified inertial method for solving equilibrium problems and fixed point problem in Hadamard manifold
Viscosity extragradient with modified inertial method for solving equilibrium problems and fixed point problem in Hadamard manifold
In this article, we propose a viscosity extragradient algorithm together with an inertial extrapolation method for approximating the solution of pseudomonotone equilibrium and fixed point problem of a nonexpansive mapping in the setting of a Hadamard manifold. We prove that the sequence generated by our iterative method converges to a solution of the above problems under some mild conditions. Finally, we outline some implications of our results and present several numerical examples showing the implementability of our algorithm. The results of this article extend and complement many related results in linear spaces.
47J25, 65J15, 65K15, 90C33, Equilibrium problem, Fixed point problems, Hadamard manifold and extragradient algorithm, Nonexpansive mapping, Viscosity
Ndlovu, P.V.
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Jolaoso, L.O.
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Aphane, M.
dffa9fec-78a2-44d4-960f-26395b2a3555
Abass, H.A.
aa6a64a5-79bf-41dd-a5d0-0681fdc1e9ec
13 February 2024
Ndlovu, P.V.
b8ecfcd0-2938-45b2-a3ab-6eacf29e6c3c
Jolaoso, L.O.
102467df-eae0-4692-8668-7f73e8e02546
Aphane, M.
dffa9fec-78a2-44d4-960f-26395b2a3555
Abass, H.A.
aa6a64a5-79bf-41dd-a5d0-0681fdc1e9ec
Ndlovu, P.V., Jolaoso, L.O., Aphane, M. and Abass, H.A.
(2024)
Viscosity extragradient with modified inertial method for solving equilibrium problems and fixed point problem in Hadamard manifold.
Journal of Inequalities and Applications, 2024 (1), [21].
(doi:10.1186/s13660-024-03099-0).
Abstract
In this article, we propose a viscosity extragradient algorithm together with an inertial extrapolation method for approximating the solution of pseudomonotone equilibrium and fixed point problem of a nonexpansive mapping in the setting of a Hadamard manifold. We prove that the sequence generated by our iterative method converges to a solution of the above problems under some mild conditions. Finally, we outline some implications of our results and present several numerical examples showing the implementability of our algorithm. The results of this article extend and complement many related results in linear spaces.
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s13660-024-03099-0
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Accepted/In Press date: 29 January 2024
Published date: 13 February 2024
Keywords:
47J25, 65J15, 65K15, 90C33, Equilibrium problem, Fixed point problems, Hadamard manifold and extragradient algorithm, Nonexpansive mapping, Viscosity
Identifiers
Local EPrints ID: 488897
URI: http://eprints.soton.ac.uk/id/eprint/488897
ISSN: 1025-5834
PURE UUID: e95bc319-611c-4e57-98be-f06049a3d286
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Date deposited: 09 Apr 2024 16:33
Last modified: 10 Apr 2024 02:07
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Contributors
Author:
P.V. Ndlovu
Author:
M. Aphane
Author:
H.A. Abass
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