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

Abstract

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 T h has the Hyers–Ulam stability.