Bulletin of the
Korean Mathematical Society BKMS

We show that two concepts of h-stability and h-stabil-ity in variation for nonlinear difference systems are equivalent by using the concept of $n_\infty$-summable similarity of their associated variational systems. Also, we study h-stability for perturbed nonlinear system $y(n+1)=f(n,y(n))+g(n,y(n),Sy(n))$ of nonlinear difference system $x(n+1)=f(n,x(n))$ using the comparison principle and extended discrete Bihari-type inequality.

Keywords: $n_\infty$-summable similarity, $h$-system, Bihari-type inequality, comparison principle

MSC numbers: 39A11