- Open Access
Erratum to: Some new theorems of expanding mappings without continuity in cone metric spaces
© Xu et al.; licensee Springer. 2014
- Received: 28 July 2014
- Accepted: 28 July 2014
- Published: 19 August 2014
The original article was published in Fixed Point Theory and Applications 2013 2013:3
In this note we correct some errors that appeared in the article (Han and Xu in Fixed Point Theory Appl. 2013:3, 2013) by modifying some conditions in the main theorems and corresponding corollaries.
- cone metric space
- expanding mapping
- common fixed point
Upon critical examination of the main results and their proofs in , we note several critical errors in the conditions of the main theorems in . These errors lead to subsequent errors in the corresponding corollaries in .
In this note, we would like to supplement several conditions, which are used in their proofs but not referred to in the conditions of the main results, to achieve our claim.
The following theorem is a modification to [, Theorem 2.1]. The proof is the same as that in . We will attain the desired goal by adding two conditions to that in [, Theorem 2.1]. We state that Theorem 2.1 in  is replaced by the following theorem.
for all , where () satisfy , , and . Then f has a fixed point.
must be valid.
for all , where () satisfy , , and , . Then f and g have a common fixed point.
Accordingly, the following two corollaries are modifications to Corollary 2.2 and Corollary 2.6 in , and we state that the latter corollaries are replaced by the former ones, respectively.
for all , where , and . Then f has a fixed point.
for all , where , , and . Then f and g have a common fixed point.
The research is partially supported by the PhD Start-up Fund of Hanshan Normal University, Guangdong Province, China (No. QD20110920).
- Han Y, Xu S: Some new theorems of expanding mappings without continuity in cone metric spaces. Fixed Point Theory Appl. 2013., 2013: Article ID 3Google Scholar
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