HYERS-ULAM STABILITY FOR AN NTH ORDER DIFFERENTIAL EQUATION USING FIXED POINT APPROACH

Abstract

In this paper, we prove the Hyers-Ulam stability and the HyersUlam-Rassias stability of the nth order differential equation of the form x((n))(t) = f(t, x(t)) and x((n))(t) = f (t, x(t), x' (t), x '' (t), ..., x((n-1))(t)) with initial conditions x(a) = x(0), x' (a) = x(1), x '' (a) = x(2), ..., x((n-1))(a) = x(n-1) for all t is an element of I = [a, b] subset of R and x is an element of C-(n)( I) by using fixed point method in the sense of Cadariu and Radu.