The asymptotic stability of difference equations Original Research Article

In this paper, the linear delay difference equation xn+1 −xn = −anxn−k, where an ≥ 0 (n ≥ 0) any nonnegative coefficient sequence, is considered and its stability properties are investigated. The obtained result is extended to the nonlinear difference equation xn+1 − xn = fn(xn−k).