On the difference equation xn+1 = α+βx n-1+γxn-2+f(xn-1,xn-2)/x n

Abstract

In this note we investigate the behavior of solutions of the difference equation xn+1 = α+βxn-1+γx n-2+f(xn-1,xn-2/xn, n=0, 1, ... where α, β, γ and initial conditions x-2,x -1, x0 are positive real numbers and f: (0, ∞) 2 → (0, ∞) is a real continuous function.