Let {φn} be a sequence of rational functions with arbitrary complex poles, generated by a certain three-term recurrence relation. In this paper we show that under some mild conditions the rational functions φn form an orthonormal system with respect to a Hermitian positive-definite inner product.

Asymptotic stability for difference equations with decreasing arguments D. M. Chan , E. R. Chang , M. Dehghan , C. M. Kent , R. Mazrooei-Sebdani & H. Sedaghat To cite this article: D. M. Chan , E. R. Chang , M. Dehghan , C. M. Kent , R. Mazrooei-Sebdani & H. Sedaghat (2006) Asymptotic stability for difference equations with decreasing arguments, Journal of Difference Equations and Applications,...

We extend and give short proofs of some recent results regarding some classes of rational difference equations.

In this paper, we investigate the global behavior of the difference equation xn+1 = αxn−1 β + γ t ∑

A discrete n-species Schoener competition system with time delays and feedback controls is proposed. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.