Summary: We obtain convergence theorems of both an implicit iteration process and an explicit iteration process for an asymptotically nonexpansive semigroup in a Banach space with a uniform normal structure and a uniformly Gâteaux differentiable norm.
Editor’s remark. The authors do not mention their paper [Nonlinear Funct. Anal. Appl. 15, No. 4, 533–543 (2010; Zbl 1301.47092)] which contains analogous results in a slightly different situation.