# Erratum to: An implicit method for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces

The Original Article was published on 04 December 2014

Unfortunately, the original version of this article [1] contained an error. In TheoremÂ 3.1 the condition â€˜left amenableâ€™ is required instead of the condition â€˜left invariantâ€™, because the authors used the LemmaÂ 2.2 and in that lemma â€˜Xâ€™ is amenable.

The correct TheoremÂ 3.1 is correctly included in full in this erratum:

FormalPara Theorem 3.1

Let S be a semigroup. Let C be a nonempty compact convex subset of a real strictly convex and reflexive and smooth Banach space E. Suppose that $$\mathcal{S}=\{T_{s}:s\in S\}$$ is a representation of S as nonexpansive mapping from C into itself such that $$\operatorname{Fix}(\mathcal {S})\neq\emptyset$$. Let X be a left amenable subspace of $$B(S)$$ such that $$1\in X$$, and the function $$t\mapsto\langle T_{t}x,x^{*}\rangle$$ is an element of X for each $$x\in C$$ and $$x^{*}\in E^{*}$$. Let $$\{\mu_{n}\}$$ be a left regular sequence of means on X. Suppose that f is an Î±-contraction on C. Let $$\epsilon_{n}$$ be a sequence in $$(0, 1)$$ such that $$\lim_{n} \epsilon_{n}=0$$. Then there exists a unique sunny nonexpansive retraction P of C onto $$\operatorname{Fix}(\mathcal{S})$$ and $$x \in C$$ such that the following sequence $$\{z_{n}\}$$ generated by

$$z_{n}=\epsilon_{n} f(z_{n})+(1- \epsilon_{n})T_{\mu_{n}}z_{n}\quad( n \in\mathbb{N}),$$
(1)

strongly converges to Px.

## References

1. Hussain, N, Lashkarizadeh Bami, M, Soori, E: An implicit method for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces. Fixed Point Theory Appl. 2014, 238 (2014)

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Correspondence to Ebrahim Soori.

The online version of the original article can be found under doi:10.1186/1687-1812-2014-238.

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