## 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:10.1186/1687–1812–2012–221

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

## References

## Acknowledgements

## Author information

### Authors and Affiliations

### Corresponding author

## Additional information

### Competing interests

### Authors’ contributions

## Rights and permissions

## About this article

### Cite this article

### Keywords

- Research
- Open Access
- Published:

*Fixed Point Theory and Applications*
**volume 2013**, Article number: 8 (2013)

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

G(x,y,z)=(|x-y|+|y-z|+|z-x|)

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}].

Moreover,

\begin{array}{rcl}G(fx,fy,fz)& =& (|fx-fy|+|fy-fz|+|fz-fx|)\\ =& \frac{3}{2}(|x-y|)\ge q\left[\frac{1}{2}(|x-y|)\right]=qG(gx,gy,gz)\end{array}

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*.

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:10.1186/1687–1812–2012–221

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

The authors declare that they have no competing interests.

All authors read and approved the manuscript.

**Open Access** This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Manro, S., Kumam, P. Erratum to ‘Common fixed point theorems for expansion mappings in various abstract spaces using concept of weak reciprocal continuity’.
*Fixed Point Theory Appl* **2013**, 8 (2013). https://doi.org/10.1186/1687-1812-2013-8

Received:

Accepted:

Published:

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

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