Global attractivity of the difference equation xn+1 = α+( xn− k/ xn)

Abstract

In this paper, we investigate the global stability of all negative solutions of the difference equation x n+1=α+ x n−k x n , n=0,1,…, where α<1 is a real number, k⩾1 is an integer, and the initial conditions x − k ,…, x 0 are arbitrary real numbers. We show that the unique negative equilibrium of the equation is a global attractor with a basin that depends on certain conditions of the coefficient.