  In this paper, a strong convergence theorem for asymptotically nonexpansive
mappings in a uniformly convex and smooth Banach space is proved by using
metric projections. This theorem extends and improves the recent strong
convergence theorem due to Matsushita and Takahashi [
  Appl. Math. Comput. 196 (2008) 422-425] which was established for
nonexpansive mappings.
