Asymptotic stability for a linear difference equation with variable delay

We shall obtain sufficient conditions for the uniform stability and the global asymptotic stability of the linear difference equation with variable delay xn+1−xn+pnxn−kn=0,n N where “pn” is a sequence of nonnegative real numbers, “kn” is a sequence of nonnegative integers, and there exists a nonnegative integer k such that kn ≤ k, for n N.