Hybrid algorithm for maximal monotone operators, quasi-ϕ-nonexpansive mappings and equilibrium problems in banach spaces

In this paper, some hybrid iterative algorithms for approximating the common element of the set of solutions of an equilibrium problem, the set of common fixed points of finitely many quasi-φ-nonexpansive mappings and the set of common zeroes of finitely many maximal monotone operators in a uniformly smooth and uniformly convex Banach space are presented. Some strong convergence theorems are obtained which extend and complement the previous results. Moreover, the applications of the iterative algorithms to optimization problem and minimizer problem are demonstrated. The work done in this paper has significance in the area of economic mathematics, engineering sciences and some others.