LOCAL CONVERGENCE OF SIXTH-ORDER NEWTON-LIKE METHODS BASED ON STOLARSKY AND GINI MEANS

Stolarsky-Gini means have been used in connection to a sixth order Newton-like method to compute solutions of nonlinear equations defined on the real line [1,2,3,4]. The local convergence was shown using Taylor expansions and conditions reaching at least until the seventh derivative, although only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. In the present article we show convergence based only on the first derivative. The numerical examples justify the theoretical results.