A new hybrid projection algorithm for system of equilibrium problems and variational inequality problems and two finite families of quasi-\(\phi\)-nonexpansive mappings (Q1949428)

Summary: We introduce a modified Mann's iterative procedure by using the hybrid projection method for finding the common solution of a system of equilibrium problems for a finite family of bifunctions satisfying certain conditions, the common solution of fixed-point problems for two finite families of quasi-\(\phi\)-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.