BALL CONVERGENCE FOR A CLASS OF ROOT-FINDING METHODS IN BANACH SPACE UNDER WEAK CONDITIONS

We present the ball convergence for a class of root-finding methods in a Banach space setting of convergence order at least six. In contrast to earlier studies using hypotheses up to the second Frechet-derivative although such derivatives do not appear in the method, we only use the first derivative. Thus, we extend the applicability of these methods. In the examples, we solve systems of nonlinear equations as well as integral equations, especially in cases that cannot be covered with results from earlier studies.