In this note, we consider global asymptotic stability of the following nonlinear difference equationxn=(∏i=1v(xn-kiβi+1)+∏i=1v(xn-kiβi-1))/(∏i=1v(xn-kiβi+1)-∏i=1v(xn-kiβi-1)), n=0,1,…, whereki∈ℕ (i=1,2,…,v), v≥2,β1∈[-1,1],β2,β3,…,βv∈(-∞,+∞),x-m,x-m+1,…,x-1∈(0,∞), andm=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).
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