Hyers–Ulam stability of linear functional differential equations

In this paper, the stability of some classes of linear functional differential equations was discussed by direct method, iteration method, fixed point method and open mapping theorem. It is shown that the Hyers–Ulam stability holds true for y(n)=g(t)y(t−τ)+h(t)y(n)=g(t)y(t−τ)+h(t). The stability of functional differential equations with multiple delays of first order and general delay differential equations also have been discussed.