Stability of Volterra difference delay equations

Abstract

We study the asymptotic stability of the zero solution of the Volterra difference delay equation \begin{equation} x(n+1)=a(n)x(n)+c(n)\Delta x(n-g(n))+\sum^{n-1}_{s=n-g(n)}k(n,s)h(x(s)).\nonumber \end{equation} A Krasnoselskii fixed point theorem is used in the analysis.