Convergence of Newton-Kantorovich Approximations to an Approximate Zero.

In this paper, we prove an a posteriori and an a priori convergence theorem for Newton-Kantorovich approximations starting from an initial point x0. We apply these results to operators that are analytic at interior points of a closed ball centered at x0 and of radius R. We obtain some theorems on approximate zeros and on approximate zeros of second kind for these operators, which improve previous results. [ABSTRACT FROM AUTHOR]