A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in hadamard spaces
A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in hadamard spaces
In this work, we study a self-adaptive extragradient algorithm for approximating a common solution of a pseudomonotone equilibrium problem and fixed-point problem for multivalued nonexpansive mapping in Hadamard spaces. Our proposed algorithm is designed in such a way that its step size does not require knowledge of the Lipschitz-like constants of the bifunction. Under some appropriate conditions, we establish the strong convergence of the algorithm without prior knowledge of the Lipschitz constants. Furthermore, we provide a numerical experiment to demonstrate the efficiency of our algorithm. This result extends and complements recent results in the literature.
common fixed point, equilibrium problems, extragradient method, hadamard spaces, pseudomontone
Aremu, Kazeem Olalekan
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Jolaoso, Lateef Olakunle
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Oyewole, Olawale Kazeem
6e9e09ed-3aeb-4a42-acb3-67d7318288ec
Aremu, Kazeem Olalekan
7c8766e4-ec45-4093-baca-e79f01088056
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Oyewole, Olawale Kazeem
6e9e09ed-3aeb-4a42-acb3-67d7318288ec
Aremu, Kazeem Olalekan, Jolaoso, Lateef Olakunle and Oyewole, Olawale Kazeem
(2023)
A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in hadamard spaces.
Fixed Point Theory and Algorithms for Sciences and Engineering, 2023 (1), [4].
(doi:10.1186/s13663-023-00742-1).
Abstract
In this work, we study a self-adaptive extragradient algorithm for approximating a common solution of a pseudomonotone equilibrium problem and fixed-point problem for multivalued nonexpansive mapping in Hadamard spaces. Our proposed algorithm is designed in such a way that its step size does not require knowledge of the Lipschitz-like constants of the bifunction. Under some appropriate conditions, we establish the strong convergence of the algorithm without prior knowledge of the Lipschitz constants. Furthermore, we provide a numerical experiment to demonstrate the efficiency of our algorithm. This result extends and complements recent results in the literature.
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s13663-023-00742-1
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Accepted/In Press date: 15 March 2023
e-pub ahead of print date: 17 April 2023
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Funding Information:
The authors appreciate the support of their institutions.
Keywords:
common fixed point, equilibrium problems, extragradient method, hadamard spaces, pseudomontone
Identifiers
Local EPrints ID: 477149
URI: http://eprints.soton.ac.uk/id/eprint/477149
PURE UUID: b5cde9a1-5e9f-4094-bdba-d79b627ca144
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Date deposited: 30 May 2023 16:39
Last modified: 31 May 2023 01:57
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Contributors
Author:
Kazeem Olalekan Aremu
Author:
Olawale Kazeem Oyewole
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