Hyers-Ulam-Rassias stability of a system of first order linear recurrences

摘要

In this paper we discuss the Hyers-Ulam-Rassias stability of a system of first order linear recurrences with variable coefficients in Banach spaces. The concept of the Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. {f 72} (1978), 297--300. As an application, the Hyers-Ulam-Rassias stability of a $p$-order linear recurrence with variable coefficients is proved.