Pri 45J05, Sec 45N05, 45B05, 65L05.

A new approach for neutral Fredholm integro-differential equations in Banach spaces, using the Perov's fixed point theorem of existence, uniqueness and approximation is presented. The approximation of the solution and of its derivative is realized using the method of successive approximations and a trapezoidal quadrature rule in Banach spaces for Lipschitzian functions. The interest is focused on the error estimation.;