Toward a New Solution Technique for Pseudo-Monotone Equilibrium Problems in Banach Spaces

In this paper, we propose a novel algorithm that combines the inertial extragradient method with the hybrid projection technique to address pseudo-monotone equilibrium problems involving Bregman relatively non-expansive mappings in reflexive Banach spaces. We establish strong convergence of the algorithm under mild assumptions on the cost operators. Furthermore, the proposed method proves to be effective for solving variational inequality problems.

Keywords:

Equilibrium problem , Bregman projection , pseudo-monotone bifunction