On the existence and approximation of solutions of generalized equilibrium problem on Hadamard manifolds

O. K. Oyewole, L. O. Jolaoso, K. O. Aremu*, M. Aphane

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the existence of solution of the generalized equilibrium problem (GEP) in the framework of an Hadamard manifold. Using the KKM lemma, we prove the existence of solution of the GEP and give the properties of the resolvent function associated with the problem under consideration. Furthermore, we introduce an iterative algorithm for approximating a common solution of the GEP and a fixed point problem. Using the proposed method, we obtain and prove a strong convergence theorem for approximating a solution of the GEP, which is also a fixed point of a nonexpansive mapping under some mild conditions. We give an application of our convergence result to a solution of the convex minimization problem. To illustrate the convergence of the method, we report some numerical experiments. The result in this paper extends the study of the GEP from the linear settings to the Hadamard manifolds.

Original languageEnglish
Article number142
JournalJournal of Inequalities and Applications
Volume2022
Issue number1
DOIs
Publication statusPublished - 2022

Keywords

  • Equilibrium problem
  • Extragradient method
  • Hadamard manifold
  • Pseudomonotone
  • Riemannian manifold

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