Using Schaefer’s fixed-point theorem, enabling us to show that if there is an a priori bound on all possible T -periodic solutions of an infinite delay Volterra difference equation, then there is a T -periodic solution. We apply our results to scalar infinite delay Volterra difference equations in which, the a priori bound is established by means of nonnegative definite Lyapunov functionals. AM...

In this paper, a Banach phase space containing BC(−∞, 0] and contained in C(−∞, 0] is defined with which existence of a solution and convergence of a discrete scheme are proved for an infinite delay differential equation.