TY - JOUR
T1 - A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in Hadamard spaces
AU - Aremu, Kazeem Olalekan
AU - Jolaoso, Lateef Olakunle
AU - Oyewole, Olawale Kazeem
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023/12
Y1 - 2023/12
N2 - 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.
AB - 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.
KW - Common fixed point
KW - Equilibrium problems
KW - Extragradient method
KW - Hadamard spaces
KW - Pseudomontone
UR - http://www.scopus.com/inward/record.url?scp=85153314748&partnerID=8YFLogxK
U2 - 10.1186/s13663-023-00742-1
DO - 10.1186/s13663-023-00742-1
M3 - Article
AN - SCOPUS:85153314748
SN - 1687-1820
VL - 2023
JO - Fixed Point Theory and Algorithms for Sciences and Engineering
JF - Fixed Point Theory and Algorithms for Sciences and Engineering
IS - 1
M1 - 4
ER -