Existence of bounded solutions for almost linear Volterra difference equations using fixed point theory and Lyapunov functionals

Abstract

We obtain sufficient conditions for the boundedness of solutions of the almost linear Volterra difference equation
 \begin{align*} \Delta x(n)=a(n)h(x(n))+\sum^{n-1}_{k=0}c(n, k)g(x(k)) \end{align*}
 using Krasnoselskii's fixed point theorem. Also, we will display a Lyapunov functional that yield boundedness of solution and compare both methods.