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

*Fixed Point Theory and Applications*
**volumeÂ 2015**, ArticleÂ number:Â 203 (2015)

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€˜*X*â€™ is amenable.

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

*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*

*strongly converges to*
*Px*.

## References

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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## Additional information

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

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Hussain, N., Lashkarizadeh Bami, M. & Soori, E. Erratum to: An implicit method for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces.
*Fixed Point Theory Appl* **2015**, 203 (2015). https://doi.org/10.1186/s13663-015-0450-y

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DOI: https://doi.org/10.1186/s13663-015-0450-y