Hybrid projection method for generalized mixed equilibrium problem and fixed point problem of infinite family of asymptotically quasi-ϕ-nonexpansive mappings in Banach spaces

In this paper, we consider a hybrid projection method for finding a common element in the set of fixed points of a infinite family of asymptotically quasi-ϕ-nonexpansive mappings and in the set of solutions of a generalized mixed equilibrium problem. Some strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec–Klee property. The results presented in the paper improve and extend some recent results.