Abstract: Using the Schauder’s fixed point theorem and the Banach contraction mapping principle, we discussed a class of integrodifferential equation with the KurzweilHenstockStieltjes integral, and proved the existence and uniqueness of their solutions.

Key words: integrodifferential equation, KurzweilHenstockStieltjes integral, Schauder’s fixed point theorem, Banach contraction mapping principle