# 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.

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.