The purpose of this paper is to establish existence results of nonoscillatory solutions of the following \(n\)-th order delay differential equation: \[ \frac{d^n}{dt^n}[x(t)+cx(t-\tau)]+(-1)^{n+1}f(t,x(t-\gamma_1),\dots,x(t-\gamma_k))=g(t) \] The authors construct Mann-type iterative approximation schemes with error estimates between the approximate solutions and the nonoscillatory solutions.