A golden ratio technique for equilibrium problem in reflexive Banach spaces
Hammed A. Abass, Abubakar Adamu, Olawale K. Oyewole, Maggie Aphane · Demonstratio Mathematica · 2025
Abstract In this article, we present a self-adaptive subgradient extragradient method for approximating solutions of equilibrium problems with pseudomonotone and Lipschitz type bifunctions in the context of reflexive Banach spaces. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges weakly to the solution of equilibrium problem. We improve the convergence efficiency of our proposed algorithm by introducing a new step size and a golden ratio technique. Finally, we demonstrate through numerical experiments the performance of our iterative algorithm in comparison with existing methods. The result obtained in this article extends and improves many recent results in the literature.