Approximating fixed points of nonexpansive mappings in a Banach space by metric projections

In this paper, a strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem is different from the recent strong convergence theorem due to Xu [H.K. Xu, Strong convergence of approximating fixed point sequences for nonexpansive mappings, Bull. Aust. Math. Soc. 74 (2006) 143–151] which was established by generalized projections.