NOTE ON THE HYERS-ULAM-RASSIAS STABILITY OF THE FIRST ORDER LINEAR DIFFERENTIAL EQUATION

Abstract

Let X be a complex Banach space and I an open interval. We prove the stability result in the sense of Hyers-Ulam-Rassias of the X-valued differential equation y'(t) + p(t)y(t) + q(t) = 0. If f: I->X is an approximate solution of y'+py+q = 0, then to each s in I there corresponds an exact solution g_s: I- X of the differential equation above such that gs is near to f.