Hyers-Ulam-Rassias stability of non-linear delay differential equations

In this paper, we prove the Hyers-Ulam-Rassias stability and Hyers-Ulam stability of delay differential equation of the form \[y⁽ⁿ⁾=F(t,\{y⁽ⁱ⁾(t)\}ⁿ⁻¹ᵢ₌₀,\{y⁽ⁱ⁾(t-λ)\}ⁿ⁻¹ᵢ₌₀),\] with Lipschitz condition by using fixed point approach. The results of the paper generalize most of the results concerning the stability of delay differential equations in the existing literature.