AbstractIn this paper we focus on three fixed point theorems and an integral equation. Schaefer's fixed point theorem will yield a T‐periodic solution of(0.1)x(t)= a(t)+tt‐hD(t,s)g(s,x(s))dsifDandgsatisfy certain sign conditions independent of their magnitude. A combination of the contraction mapping theorem and Schauder's theorem (known as Krasnoselskii's theorem) will yield a T‐periodic solution of(0.2)x(t)= f(t,x(t)) +tt‐hD(t,s)g(s,x(s))dsiffdefines a contraction and ifDandgare small enough.We prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T‐periodic solution of (0.2) when / defines a contraction mapping, whileDandgsatisfy the aforementioned sign c