Global Asymptotic Stability of a Family of Nonlinear Difference Equations

• Main Author: Maoxin Liao
• Format: Article
• Language: English
• Published: Hindawi Limited 2013-01-01
• Series: Discrete Dynamics in Nature and Society
• Online Access: http://dx.doi.org/10.1155/2013/750852

In this note, we consider global asymptotic stability of the following nonlinear difference equation xn=(∏i=1v(xn-kiβi+1)+∏i=1v(xn-kiβi-1))/(∏i=1v(xn-kiβi+1)-∏i=1v(xn-kiβi-1)),  n=0,1,…, where ki∈ℕ  (i=1,2,…,v),  v≥2, β1∈[-1,1], β2,β3,…,βv∈(-∞,+∞), x-m,x-m+1,…,x-1∈(0,∞), and m=max1≤i≤v{ki}. Our result generalizes the corresponding results in the recent literature and simultaneously conforms to a conjecture in the work by Berenhaut et al. (2007).