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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 5156314, 7 pages
Research Article

An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

1School of Automation, Hangzhou Dianzi University, Zhejiang 310018, China
2Jiangxi E-Commerce High Level Engineering Technology Research Centre, Jiangxi University of Finance and Economics, Nanchang 330013, China
3Department of Mathematics Education, Kyungnam University, Changwon, Gyeongnam 631-701, Republic of Korea
4School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China

Correspondence should be addressed to Ke Ding

Received 29 June 2017; Accepted 27 September 2017; Published 9 November 2017

Academic Editor: Pasquale Candito

Copyright © 2017 Ke Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with designing a new iteration scheme associated with a given scheme for contraction mappings. This new scheme has a similar structure to that of the given scheme, in which those two iterative schemes converge to the same fixed point of the given contraction mapping. The positive influence of feedback parameters on the convergence rate of this new scheme is investigated. Moreover, the derived convergence and comparison results can be extended to nonexpansive mappings. As an application, the derived results are utilized to study the synchronization of logistic maps. Two illustrated examples are used to reveal the effectiveness of our results.