Invariance of Hyers-Ulam stability of linear differential equations and its applications

Abstract

We prove that the generalized Hyers-Ulam stability of linear differential equations of nth order (defined on I) is invariant under any monotone one-to-one correspondence : I J which is n times continuously differentiable. Moreover, using this result, we investigate the generalized Hyers-Ulam stability of the linear differential equation of second order and the Cauchy-Euler equation.