On the recursive sequence xn+1=(alpha + beta xn-k+1) / (A + Bxn-k+1 + Cxn-2k+1)
Abstract In this paper, we study the global asymptotic stability, invariant intervals, the character of semicycles, and the boundedness of all positive solutions of the higher order nonlinear difference equation x n + 1 = α + β x n - k + 1 A + Bx n - k + 1 + Cx n - 2 k + 1 , n = 0 , 1 , … , where A, B, C and α, β are positive, k ∈ {1, 2, 3, … }, and the initial conditions x−2k+1, … , x−1, x0 are positive real numbers. We show that the unique positive equilibrium of the equation is globally asymptotically stable. Finally, we present some informative examples.