Stability results for difference equations of Volterra type (Q923277)

This paper is concerned with the stability of nonlinear Volterra difference equations of type \(x(n+1)-x(n)=f(n,x(n))+\sum^{n- 1}_{s=n_ 0}g(n,s,x(s)),\) \(x(n_ 0)=x_ 0\), with suitable maps f and g. By comparing the mentioned equation with certain linear Volterra difference equation, the authors are able to impose propriate conditions on f and g to ensure the asymptotic stability of the trivial solution of the above nonlinear difference equations.