Li, Wantong; Zhang, Yanhong; Su, Youhui Global attractivity in a class of higher-order nonlinear difference equation. (English) Zbl 1168.39301 Acta Math. Sci., Ser. B, Engl. Ed. 25, No. 1, 59-66 (2005). In this paper the global attractivity of the nonlinear difference equation \[ x_{n+1}=\frac{a+bx_{n}}{A+x_{n-k}},\quad n=0,1,... \] is investigated, where \(a,b,A \in (0,\infty),k\) are positive numbers and the initial conditions \(x_{-k},...,x_{-1}\) and \(x_0\) are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary the result gives a positive confirmation of the conjecture presented by Kocic and Ladas. Reviewer: Ahmed Hegazi (Mansoura) Cited in 5 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis Keywords:difference equation; global attractivity; stability; equilibrium PDF BibTeX XML Cite \textit{W. Li} et al., Acta Math. Sci., Ser. B, Engl. Ed. 25, No. 1, 59--66 (2005; Zbl 1168.39301) Full Text: DOI OpenURL