... resultsIn the rest of the paper we denote the set of real numbers as R,andR+=[0,∞)isasubset of R. Dom(f)andIm(f) denote the definition domain and the image of f,respectively.Theorem 2.1: ... prove the global existence of the solu-tions of a delay differential equation, while in the second example, we will obtain the bound of the solutions of an integral equation.For the sake of proving ... completed the proof.Remark 4:Ifh(s, t) ≡ 0, a1(t)=a2(t)=a(t), then Theorem 2.2 becomes Theorem C[10, Theorem 1].Now we will apply the concept of establishing Theorem 2.2 to the situation...