The convex feasibility problem (CFP) of finding a point in the nonempty intersection ⋂ i = 1 N C i is considered, where N ⩾ 1 is an integer and the C i 's are assumed to be convex closed subsets of a Banach space E . By using hybrid iterative methods, we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, we apply our results for solving convex feasibility problems in Banach spaces.