A characterization of Hyers-Ulam stability of first order linear differential operators

Let X be a complex Banach space and h : R --> C a continuous function. Let T-h : C-1 (R, X) --> C(R, X) be the linear differential operator defined by T(h)u = u' + hu. We give a necessary and sufficient condition in order that the operator Th has the Hyers-Ulam stability. (C) 2003 Elsevier Inc. All rights reserved.