Hyers-Ulam stability of linear differential equations of first order, III

Abstract

Let X be a complex Banach space and let I = (a, b) be an open interval. In this paper, we will prove the generalized Hyers-Ulam stability of the differential equation ty'(t) +alpha y(t) + beta t(r)x(0) = 0 for the class of continuously differentiable functions f : I -> X, where alpha, beta and r are complex constants and x(0) is an element of X. By applying this result, we also prove the Hyers-Ulam stability of the Euler differential equation of second order. (c) 2005 Elsevier Inc. All rights reserved.