A hybrid scheme for fixed points of a countable family of generalized non-expansive-type maps and generalized mixed equilibrium problems

Let $\mathrm{\Omega }$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $\mathcal{X}$ with dual space ${\mathcal{X}}^{\ast }$. This article presents a hybrid algorithm for finding a common element of the set of solutions to a generalized mixed equilibrium problem and the set of common fixed points of a family of a general class of nonlinear nonexpansive maps. The results obtained were employed to study optimization problem. Our results and its applications complement, generalize, and extend several results in literature.