be a mapping. The author studies the approximate solution of the equation
by means of the iterative method for
for some sequence
. He gives an affine invariant condition involving
which ensures the local convergence of (*) to a solution of
. Moreover he deduces a radius of convergence result for (*) which is shown to be sharp for both Newton’s method and the general difference Newton-like method. The results are applied to the latter two methods and the general Newton-like method in which the iterates are perturbed by the presense of rounding errors. No numerical example.