Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups Original Research Article

The Mann iterations for nonexpansive mappings have in general only weak convergence in a Hilbert space. We modify an iterative method of Mannʹs type introduced by Nakajo and Takahashi [Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372–379] for nonexpansive mappings and prove strong convergence of our modified Mannʹs iteration processes for asymptotically nonexpansive mappings and semigroups.