The Hyers–Ulam stability constants of first order linear differential operators

Let X be a complex Banach space, h a complex-valued continuous function on the real line R and Th :C1(R,X)→C(R,X) the linear differential operator defined by Thu = u + hu. We completely determine the Hyers–Ulam stability constant of Th.  2004 Elsevier Inc. All rights reserved.