Weighted Hyers-Ulam Stability for Nonlinear Nonautonomous Difference Equations - Dragičević, Davor (Sarajevo Journal of Mathematics, 2024)
Let $(A_m)_{m\in \mathbb{Z}}$ be a sequence of bounded linear operators acting on an arbitrary Banach space $X$ and admitting an exponential dichotomy. Furthermore, let $f_m \colon X→ X$, $m\in \mathbb{Z}$ be a sequence of Lipschitz maps. Provided that the Lipschitz constants of $f_m$ are uniformly small, we show that a nonlinear difference equation $x_{m+1} = A_mx_m +f_m(x_m), m\in \mathbb{Z}$ exhibits various types of the Hyers-Ulam stability property.