A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings

Abstract EN

We introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi-ϕ-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space.

Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions.

Our result presented in this paper improves and generalizes some well-known results in the literature.