Block methods for a convex feasibility problem in a Banach space

In this paper, a convex feasibility problem is investigated based on a block method. Strong conver-gence theorems for common solutions of equilibrium problems and generalized asymptotically quasi-φ-nonexpansive mappings are established in a strictly convex and uniformly smooth Banach space which also has the Kadec-Klee property. The results obtained in this paper unify and improve many corresponding results announced recently.