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

The Original Article was published on 13 September 2010

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)".

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 819269

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Acknowledgements

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

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Correspondence to M Hasan.

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The online version of the original article can be found at 10.1155/2010/819269

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Imdad, M., Tanveer, M. & Hasan, M. Erratum to "Some common fixed point theorems in Menger PM spaces". Fixed Point Theory Appl 2011, 28 (2011). https://doi.org/10.1186/1687-1812-2011-28

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