Ball convergence theorems for iterative methods under weak conditions

Abstract

We revisit a Weerakoon type iterative method for solving equations. Earlier studies have used higher order derivatives not appearing in the method for the convergence analysis. But this way the usage of the method is restricted though it may converge. That is why in order to extend its applicability, we only use hypotheses on the first derivative that actually is on the method. The fifth order of convergence has also been carried out on the finite dimensional Euclidean space. But our analysis involves more general setting of Banach space valued operators. Our idea can be used to extend the applicability of other methods along the same lines.