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# Correction: A fixed point theorem for cyclic generalized contractions in metric spaces. Fixed Point Theory and Applications 2012, 2012:122

- Maryam A Alghamdi
^{1}, - Adrian Petruşel
^{2}and - Naseer Shahzad
^{3}Email author

**2013**:39

https://doi.org/10.1186/1687-1812-2013-39

© Alghamdi et al.; licensee Springer. 2013

**Received: **31 January 2013

**Accepted: **10 February 2013

**Published: **26 February 2013

## Abstract

The purpose of this short note is to present some corrections and clarifications concerning the proof of the main result given in the above mentioned paper.

## Keywords

- Point Theorem
- Initial Point
- Differential Geometry
- Fixed Point Theorem
- Point Theory

Concerning the text and the proof of the main result (Theorem 2.2), we would like to do the following corrections and clarifications:

(1) In Theorem 2.2, an additional hypothesis is needed, namely:

(3) On page 5, to prove that the Picard iteration converges to ${x}^{\ast}$, we have to do as follows.

*f*has a unique fixed point (denoted by ${x}^{\ast}$) and the sequence ${({x}_{n})}_{n\in \mathbb{N}}$ converges to a certain $y\in {\bigcap}_{i=1}^{m}{A}_{i}$. We will show that

*y*is also a fixed point of

*f*. For this purpose, we have

This shows that *y* is a fixed point of *f* and, thus, $y={x}^{\ast}$.

## Declarations

## Authors’ Affiliations

## Copyright

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.