Weighted Hyers-Ulam Stability for Nonlinear Nonautonomous Difference Equations - Dragičević, Davor (Sarajevo Journal of Mathematics, 2024)
Let (A_m)_mZ be a sequence of bounded linear operators acting on an arbitrary Banach space X and admitting an exponential dichotomy. Furthermore, let f_m X→ X, mZ 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), mZ exhibits various types of the Hyers-Ulam stability property.