On the Strong Convergence of Combined Generalized Equilibrium and Fixed Point Problems in a Banach Space

This work develops and analyzes an iterative method to solve the combined generalized equilibrium and fixed point problems involving two relatively nonexpansive mappings. We establish that the generated sequence converges strongly to a shared solution within a two-uniformly convex and uniformly smooth real Banach space. We also highlight some immediate consequences of the main result. To confirm the algorithm’s efficiency, a numerical example is provided. Furthermore, the practical utility of the proposed algorithm is illustrated using comprehensive tables and figures.