In the present paper, we are concerned to prove under some hypothesis the existence of fixed points of the operator L defined on C(I) by Lu(t) = ∫ w 0 G(t, s)h(s) f (u(s))ds, t ∈ I, ω ∈ {1,∞}, where the functions f ∈ C([0,∞); [0,∞)), h ∈ C(I; [0,∞)), G ∈ C(I × I) and I = [0, 1], if ω = 1,I = [0,∞), if ω = ∞. By using Guo Krasnoselskii fixed point theorem, we establish the existence of at least one fixed point of the operator L.