Necessary and sufficient conditions are obtained for the asymptotic stability of difference equations of advanced typen of the form x(n) - ax(n+1) + bx(n+k) = 0, n = 0, 1, .. where a and b are arbitrary real numbers and k > 1. For a = 1, we establish an analogue of a result by Levin and May.
Dannan, F. M., & Elaydi, S. N. (2004). Asymptotic stability of linear difference equations of advanced type. Journal of Computational Analysis and Applications, 6, 173-187.
Journal of Computational Analysis and Applications