On an open question of V. Colao and G. Marino presented in the paper “Krasnoselskii–Mann method for non-self mappings”

Let H be a Hilbert space and let C be a closed convex nonempty subset of H and [Formula: see text] a non-self nonexpansive mapping. A map [Formula: see text] defined by [Formula: see text] . Then, for a fixed [Formula: see text] and for [Formula: see text] , Krasnoselskii–Mann algorithm is defined by [Formula: see text] where [Formula: see text] . Recently, Colao and Marino (Fixed Point Theory Appl 2015:39, 2015) have proved both weak and strong convergence theorems when C is a strictly convex set and T is an inward mapping. Meanwhile, they proposed a open question for a countable family of non-self nonexpansive mappings. In this article, authors will give an answer and will prove the further generalized results with the examples to support them.