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

Kazeem Olalekan Aremu, Lateef Olakunle Jolaoso, Olawale Kazeem Oyewole*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Article number4
JournalFixed Point Theory and Applications
Volume2023
Issue number1
DOIs
Publication statusPublished - Dec 2023

Keywords

  • Common fixed point
  • Equilibrium problems
  • Extragradient method
  • Hadamard spaces
  • Pseudomontone

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