On the Asymptotic Stability of the Nonlinear Difference Equation System

In this paper, we obtain some new results on the equi-boundedness of solutions and asymptotic stability for a class nonlinear difference systems with variable delay form x(n+1)=ax(n)+B(n)F(x(n−m(n))), n=0,1,2,...x(n+1)=ax(n)+B(n)F(x(n−m(n))),\ \ n=0,1,2,... where FF is real valued vector function, m:Z→Z+,m:Z→Z+, which bounded function maximum value mm kk k×kk×k coefficient matrix. We carry out proof our by using Banach fixed point theorem use these to determine conditions an example.