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Erratum to ‘Common fixed point theorems for expansion mappings in various abstract spaces using concept of weak reciprocal continuity’
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 because and . So, Example 1 in paper [1] is replaced by the following example.
Example 1 Let be a G-metric space, where and
for all .
Define by and for all .
Then, clearly, as and .
Moreover,
for 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 . However, the maps are compatible. Thus, all the conditions of Theorem 2 are satisfied and is the unique common fixed point of f and g.
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
Acknowledgements
The authors are grateful to Prof. Ravindra K. Bisht for pointing out some of these errors.
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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
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DOI: https://doi.org/10.1186/1687-1812-2013-8