Rate of convergence of solutions of rational difference equation of second order

Abstract

We investigate the rate of convergence of solutions of some special cases of the equation xn+1=(α+βxn+γxn−1)/(A+Bxn+Cxn−1), n=0,1,…, with positive parameters and nonnegative initial conditions. We give precise results about the rate of convergence of the solutions that converge to the equilibrium or period-two solution by using Poincaré's theorem and an improvement of Perron's theorem.