Hyers-Ulam Stability of the Delay Equationy'(t)=λy(t-τ)

We investigate the approximate solutions y:[−τ,∞)→Rof the delay differential equation y'(t)=λy(t-τ)(t∈[0,∞))with an initial condition, where λ>0and τ>0are real constants. We show that they can be “approximated” by solutions of the equation that are constant on the interval [-τ,0]and, therefore, have quite simple forms. Our results correspond to the notion of stability introduced by Ulam and Hyers