Stability properties and existence of almost periodic solutions of volterra difference equations

Abstract

In order to obtain the existence of periodic and almost periodic solutions of Volterra difference equation: $ x(n+1)=f(n,x(n))+\sum_{s=-\infty}^{n}F(n,s,x(n+s),x(n)) $, we consider certain two stability properties, which are referred to as (K, $ \rho $)-weakly uniformly asymptotically stable and (K, $ \rho $)-uniformly asymptotically stable.