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 Th :C1(R,X)→ C(R,X) be the linear differential operator defined by Thu = u + hu. We give a necessary and sufficient condition in order that the operator Th has the Hyers–Ulam stability.  2003 Elsevier Inc. All rights reserved.