Global asymptotic behavior of solutions of a forced delay difference equation

In this paper, we consider the nonautonomous forced delay difference equation Δxn = pnf(xn − k) + rn, N = 0,1,2,…, where the forcing term {rn} is a sequence of real numbers, {pn} a sequence of positive real numbers, k a nonnegative integer. We obtain new sufficient conditions so that every solution of the equation converges to zero. When we apply our results to some well-known delay difference population models, the corollaries improve some recent results.