Abstract
In this paper, we investigate the global asymptotic stability, the periodicity nature and the boundedness character of the positive solutions of the difference equation x(n+1) = (alpha + beta x(n-k))/(gamma - xn) where n = 0, 1, 2,... and k is an element of{1, 2,...}. The parameters alpha >= 0,gamma, beta > 0 and the initial conditions x-k, x-k+ 1,..., x-1, x0 are real positive numbers. We show that the positive equilibrium point of this equation is a global attractor with a basin that depends on certain conditions posed on the coefficients alpha, beta,gamma.