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Consider the difference equation xn+1 = (α + Σki=0 aixn-i)/(β + Σki=0 bixn-i), n = 0, 1, . . ., where all parameters α, β, ai,bi, i = 0, 1,…., k, and the initial conditions xi, i ∈ {−k, …, 0} are nonnegative real numbers. We investigate the asymptotic behavior of the solutions of the considered equation. We give easy-to-check conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation.

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This work is licensed under a Creative Commons Attribution 3.0 License.