Open Access

Erratum to "Some common fixed point theorems in Menger PM spaces"

Fixed Point Theory and Applications20112011:28

https://doi.org/10.1186/1687-1812-2011-28

Received: 6 May 2011

Accepted: 10 August 2011

Published: 10 August 2011

The original article was published in Fixed Point Theory and Applications 2010 2010:819269

On critical examination of the results given in our paper [1], we notice some minor errors except a crucial one. In all, we need to carry out the following corrections:

1. Following condition must be added to statement of Lemma 3.1 and Theorem 3.3. (*) B(y n ) converges for every sequence {y n } in X whenever T(y n ) converges (or A(x n ) converges for every sequence {x n } in X whenever S(x n ) converges).

2. Theorem 3.13 follows in view of Example 2.2 and Theorem 3.5, and henceforth an independent proof is not required as given in [1].

3. Remarks 3.6 and 3.10 are not relevant to the results as claimed in respective remarks and hence stand deleted.

4. The following typing errors are noticed in Examples 3.16 and 3.17:

(i) 'In Examples 3.16 and 3.17 "a, b [0, 2)" should be "a, b [0, 1]",

(ii) in Example 3.16. 'A(X) = {1} {1, 2/3} = S(X)" should be "A(X) = {1} {1, 1/3} = T (X)",

(iii) in Example 3.17 "A(X) = {1, 3/4} {1, 2/3} = S(X)" should be "A(X) = {1, 3/4} {1, 1/3} = T(X)" and

(iv) in Example 3.17 "B(X) = {1, 1/2} {1, 1/3} = T(X)" should be "B(X) = {1, 1/2} {1, 2/3} = S(X)".

Notes

Declarations

Acknowledgements

All the authors are grateful to Prof. Dorel Mihet for pointing out some of these errors.

Authors’ Affiliations

(1)
Department of Mathematics, Aligarh Muslim University
(2)
School of Computer & Systems Sciences, Jawaharlal Nehru University
(3)
Department of Applied Mathematics, Aligarh Muslim University

References

  1. Imdad M, Tanveer M, Hasan M: Some common fixed point theorems in Menger PM spaces. Fixed Point Theory Appl 2010, 14. Art. ID 819269Google Scholar

Copyright

© Imdad et al; licensee Springer. 2011

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.