On a nonlinear Volterra integral equation in a Banach space

The equation u(t) + ∝₀^tk(t ? s)g(s) ds?f(t), t ? 0, is studied in a real Banach space with uniformly convex dual. Conditions, sufficient for the existence of a unique solution, are given for the operatorvalued kernel k, the nonlinear m-accretive operators g(t) and the function f. The case when k is realvalued, g(t) ≡ g and X a reflexive Banach space is also considered. These results extend earlier results by Barbu, Londen and MacCamy.