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# Erratum to ‘Common fixed point theorems for expansion mappings in various abstract spaces using concept of weak reciprocal continuity’

- Saurabh Manro
^{1}Email author and - Poom Kumam
^{2}

**2013**:8

https://doi.org/10.1186/1687-1812-2013-8

© Manro and Kumam; licensee Springer 2013

**Received:**18 December 2012**Accepted:**22 December 2012**Published:**9 January 2013

## Keywords

- Point Theorem
- Differential Geometry
- Fixed Point Theorem
- Computational Biology
- Common Fixed Point

On critical examination of the results given in our paper [1], we notice one crucial error. We need to carry out the following correction.

Example 1 given in paper [1] is wrong as $g(X)\not\subset f(X)$ because $f(X)=\{2,6\}$ and $g(X)=[2,20]$. So, Example 1 in paper [1] is replaced by the following example.

**Example 1**Let $(X,G)$ be a

*G*-metric space, where $X=[0,1]$ and

for all $x,y,z\in X$.

Define $f,g:X\to X$ by $f(x)=\frac{x}{2}$ and $g(x)=\frac{x}{6}$ for all $x\in X$.

Then, clearly, $g(X)\subset f(X)$as $f(X)=[0,\frac{1}{2}]$ and $g(X)=[0,\frac{1}{6}]$.

for $1<q\le 3$ and hence, the condition (2.2) of Theorem 2 is satisfied. Also, *f* and *g* are two weakly reciprocally continuous self-maps by taking the sequence $\{{x}_{n}=\frac{1}{n}\}$. However, the maps are compatible. Thus, all the conditions of Theorem 2 are satisfied and $x=0$ is the unique common fixed point of *f* and *g*.

## Declarations

### Acknowledgements

The authors are grateful to Prof. Ravindra K. Bisht for pointing out some of these errors.

## Authors’ Affiliations

## References

- Manro S, Kumam P: Common fixed point theorems for expansion mappings in various abstract spaces using the concept of weak reciprocal continuity.
*Fixed Point Theory Appl.*2012., 2012: Article ID 221. doi:10.1186/1687–1812–2012–221Google Scholar

## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.