APPROXIMATING SOLUTIONS OF EQUATIONS BY COMBINING NEWTON-LIKE METHODS

In cases sufficient conditions for the semilocal convergence of Newton-like methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newton-like method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.