Halpern inertial subgradient extragradient algorithm for solving equilibrium problems in Banach spaces

H. A. Abass*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, we study an equilibrium problem involving a pseudomonotone bifunction in the context of uniformly smooth and 2-uniformly convex real Banach spaces. For the purpose of solving the fixed point problem of a finite family of multi-valued relatively nonexpansive mappings and the pseudomonotone equilibrium problem, we introduce an inertial subgradient extragradient method and establish its strong convergence. To increase the step size and enhance the performance of our iterative method, we use a new parameter that is independent of the inertial extrapolation method. We point out that our step size is chosen in a self-adaptive manner, making it simple to calculate our iterative algorithm without having to know the Lipschitz constants beforehand. Finally, we give some numerical results for the proposed algorithm and comparison with some other known algorithms.

Original languageEnglish
JournalApplicable Analysis
DOIs
Publication statusAccepted/In press - 2024
Externally publishedYes

Keywords

  • Equilibrium problem
  • fixed point problem
  • pseudomonotone operator
  • relatively nonexpansive mapping
  • subgradient extragradient method

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