Summary: We investigate the convergence of a Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with Fréchet differentiable norm. We also point out that the condition given by C. E. Chidume
and N. Shahzad
[Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3–4, A, 1257–1265 (2010; Zbl 1193.47065
)] is not satisfied in a real Hilbert space. We show that their results are still true under a new condition.