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 $T C\rightarrow H$$T:C H a non self nonexpansive mapping. A map $h C\rightarrow R$$h:C R defined by $h(x) \inf \lambda \ge 0 \lambda x+(1 \lambda )Tx \in C $h(x)=inf{l>=0:lx+(1 l)TxC} Then, for a fixed $x_0 \in C$$x0C and for \begin{aligned}\alpha _0} \max \left\ \frac{1}{2},h({x_0} \right\\end{aligned}$a0=max12,h(x0) Krasnoselskii Mann algorithm is defined by $x_{n+1}\alpha _n+(1 \alpha _n)Tx_n,$xn+1=an+(1 an)Txn, where \alpha _{n+1}\max \alpha _n, h(x_{x_{n+1}$an+1=max{an,h(xxn+1) 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.
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