Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations y ' = lambda y

Abstract

The aim of this paper is to prove the stability in the sense of Hyers-Ulam-Rassias of the Banach space valued differential equation y' = lambday, where lambda is a complex constant. That is, suppose f is a Banach space valued strongly differentiable function on an open interval. If f is an approximate solution of the equation y' = lambday, then there exists an exact solution of the equation near to f.