Strong convergence of shrinking projection methods for quasi-ϕ-nonexpansive mappings and equilibrium problems

The purpose of this paper is to consider the convergence of a shrinking projection method for a finite family of quasi-ϕ-nonexpansive mappings and an equilibrium problem. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property.