The Newton method for integrali equations of Hammerstein type

In this note we shall give an application of the Newton  method concernig the approximation of the solutions of the integral equations of Hammerstein type. The particular form of this equation offers the posibility, as we shall see, to obtain relative siple convergence conditions for the Newton method. On the othet hand, when the kernel of the integral operator is degerated ( or may be convenably approximated by sush on operator), then the approximation of the solution reduces to the solving of a sequence of linear systems in R, though the setting of the problem is in an infinite dimensional space.