Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 367492, 15 pages
doi:10.1155/2010/367492
Research Article

Global Behavior of Two Families of Nonlinear Symmetric Difference Equations

Wanping Liu,1 Xiaofan Yang,1,2 and Luxing Yang3

1College of Computer Science, Chongqing University, Chongqing 400044, China
2School of Computer and Information, Chongqing Jiaotong University, Chongqing 400074, China
3College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China

Received 14 May 2010; Revised 3 June 2010; Accepted 16 June 2010

Academic Editor: Josef Diblik

Copyright © 2010 Wanping Liu 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 mainly investigate the global asymptotic stability and exponential convergence of positive solutions to two families of higher-order difference equations, one of which was recently studied in Stević's paper (2010). A new concise proof is given to a quite recent result by Stević and analogous parallel result of the other inverse equation, which extend related results of Aloqeili (2009), Berenhaut and Stević (2007), and Liao et al. (2009).