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# Erratum to: ‘*n*-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces’

*Journal of Inequalities and Applications*
**volume 2013**, Article number: 368 (2013)

## Correction

(1) Page 3, line 21:

The statement ‘(ii) {lim}_{r\to t+}\varphi (r)<t for each r>0’ should be corrected as ‘(ii) {lim}_{r\to t+}\varphi (r)<t for each t>0’.

(2) Page 4, line 3:

The statement ‘… Condition 1 is satisfied.’ should be rewritten ‘… Condition 1 is satisfied and *g* is continuous.’

(3) Page 8, line 7:

The statement ‘… and using (2.20)’ should be corrected as ‘… and using (2.19)’.

(4) Page 9, line 14:

The statement ‘\le {\delta}_{j(k)+1}+{\delta}_{l(k)+1}+{t}_{k}+n\cdot \varphi (\frac{{t}_{k}}{n})’ should be corrected as ‘\le {\delta}_{j(k)+1}+{\delta}_{l(k)+1}+n\cdot \varphi (\frac{{t}_{k}}{n})’.

(5) Page 9, line 22:

The statement ‘From (2.10) and by …’ should be corrected as ‘From (2.8) and by … ’.

(6) Page 10, line 26:

‘… now the assumption (b) holds.’ should be corrected as ‘… now the assumption (ii) holds.’

(7) Page 11, line 20 (line 2 in Corollary 2) and Page 17, line 20 (line 2 in Corollary 4):

The statement ‘and there exist \varphi \in \mathrm{\Phi} such that *F*’ should be deleted.

(8) Page 11, line 22 (line 4 in Corollary 2) and Page 17, line 22 (line 4 in Corollary 4):

The statement ‘\varphi (F({x}^{1},{x}^{2},\dots ,{x}^{n}),F({y}^{1},{y}^{2},\dots ,{y}^{n}))’ should be corrected as ‘d(F({x}^{1},{x}^{2},\dots ,{x}^{n}),F({y}^{1},{y}^{2},\dots ,{y}^{n}))’.

(9) Page 16, line 27 (line 2 in Corollary 3) and Page 17, line 20 (line 2 in Corollary 4):

The statement ‘…*F* has the mixed *g*-monotone’ should be corrected as ‘…*F* has the mixed monotone’. That is, ‘*g*-’ should be deleted.

(10) Page 17, line 3:

‘\le \varphi (\frac{d(g({x}^{1}),g({y}^{1}))+d(g({x}^{2}),g({y}^{2}))+\cdots +d(g({x}^{n}),g({y}^{n}))}{n})’ should be corrected as ‘\le \varphi (\frac{d({x}^{1},{y}^{1})+d({x}^{2},{y}^{2})+\cdots +d({x}^{n},{y}^{n})}{n})’.

(11) Page 17, line 23:

‘\le \frac{m}{n}[d(g({x}^{1}),g({y}^{1}))+d(g({x}^{2}),g({y}^{2}))+\cdots +d(g({x}^{n}),g({y}^{n}))]’ should be corrected as ‘\le \frac{m}{n}[d({x}^{1},{y}^{1})+d({x}^{2},{y}^{2})+\cdots +d({x}^{n},{y}^{n})]’.

(12) Page 4, line 1:

The statement ‘{x}_{1},{x}_{2},{x}_{3},\dots ,{x}_{n}\in X’ should be corrected as ‘{x}_{1},{x}_{2},{x}_{3},\dots ,{x}_{n},{y}_{1},{y}_{2},{y}_{3},\dots ,{y}_{n}\in X’.

(13) ‘d(g({x}_{k}^{n}),g({x}_{k+2}^{n}))’ must be ‘d(g({x}_{k+1}^{n}),g({x}_{k+2}^{n}))’.

(14) Page 8, line 16:

‘\le {\delta}_{j(k)+1}+{\delta}_{l(k)+1}+d(g({x}_{j(k)+1}^{1}),g({x}_{l(k)+1}^{1}))+d(g({x}_{j(k)+1}^{2}),g({x}_{l(k)+1}^{2}))’ must be ‘\le {\delta}_{j(k)}+{\delta}_{l(k)}+d(g({x}_{j(k)+1}^{1}),g({x}_{l(k)+1}^{1}))+d(g({x}_{j(k)+1}^{2}),g({x}_{l(k)+1}^{2}))’.

(15) Page 9, line 10:

‘… with (2.26)-(2.29)’ must be ‘… with (2.26)-(2.28)’.

(16) Page 11, line 3:

‘g({x}_{k}^{1})\ge {x}^{1},g({x}_{k}^{2})\le {x}^{2},\dots ,g({x}_{k}^{n})\le {x}^{n} (If *n* is odd)’ must be ‘g({x}_{k}^{1})\le {x}^{1},g({x}_{k}^{2})\ge {x}^{2},\dots ,g({x}_{k}^{n})\le {x}^{n} (If *n* is odd)’.

## References

Ertürk M, Karakaya V:

*n*-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces.*J. Inequal. Appl.*2013., 2013: Article ID 196

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### Competing interests

The authors declare that they have no competing interests.

### Authors’ contributions

The authors made up the article together.

The online version of the original article can be found at 10.1186/1029-242X-2013-196

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**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.

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Ertürk, M., Karakaya, V. Erratum to: ‘*n*-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces’.
*J Inequal Appl* **2013**, 368 (2013). https://doi.org/10.1186/1029-242X-2013-368

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DOI: https://doi.org/10.1186/1029-242X-2013-368