The global attractivity of difference equations of nonincreasing nonlinearities with applications

The global attractivity of the unique positive equilibrium of the equation xn+1 = g(xn−k1, xn−k2, …, xn−km), n = 0,1,2,…, is investigated where g is a nonincreasing continuous function in each of its arguments and the k are positive integers. We are able to use our results to extract some important global attractivity criteria of the positive equilibria of the discrete Clark model xn+1 = αxn + f(xn−k) and the rational recursive sequence xn+1 = (a + bxn)/(A + xn−1) as well.