Contributions to the convergence analysis of nonconvex equilibrium problems

This paper establishes a successive approximation method designed to compute a point belonging simultaneously to the fixed-point set of a given mapping (relatively nonexpansive) and to the solution set of a nonconvex equilibrium problem within a Banach space. Our present findings provide a unifying generalization of numerous previously obtained results, beginning with the transition from Hilbertian structures to the more general Banach framework, and further encompassing the passage from convex analytical settings to their considerably more delicate nonconvex counterparts. We mainly extend the results proved in [27] from convex to nonconvex settings.