A note on a functional integral equation (Q675748)

This note gives an existence theorem for a nonlinear generalized Volterra integral equation of the second kind (with delay) where the unknown function \(u(t)\) arises in the integral term (in a nonlinear manner) and in an exterior term of the form \(g(t,u(f(t)))\) where \(f\) and \(g\) are given. For proving the existence of a solution, a fixed point theorem, consequence of Darbo's fixed point theorem, is used. The existence theorem is a unification of existence theorems for integral and functional equations.