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Journal of Function Spaces
Volume 2017 (2017), Article ID 2095805, 4 pages
https://doi.org/10.1155/2017/2095805
Research Article

Periodicities of a System of Difference Equations

Basic Education School, Lingnan Normal University, Zhanjiang, Guangdong 524037, China

Correspondence should be addressed to Xiaopei Li; moc.anis@33372pxil

Received 2 May 2017; Revised 3 August 2017; Accepted 1 October 2017; Published 24 December 2017

Academic Editor: Yong H. Wu

Copyright © 2017 Weizhen Quan 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.

Abstract

We study the periodicities of a system of difference equations , where initial values . We show that if are two periodic sequences, then every solution of the above system is eventually periodic with period 2. If is even, there must be one in and converges to period two solution.