A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in hadamard spaces

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).

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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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Accepted/In Press date: 15 March 2023

e-pub ahead of print date: 17 April 2023

Published date: 17 April 2023

Keywords: common fixed point, equilibrium problems, extragradient method, hadamard spaces, pseudomontone, Common fixed point, Equilibrium problems, Extragradient method, Hadamard spaces, Pseudomontone