On a novel seventh convergence order method for solving nonlinear equations and its extensions

Abstract

We extend the applicability of a novel seventh-order method for solving nonlinear equations in the setting of Banach spaces. This is done by using assumptions only on the first derivative that does appear on the method, whereas in earlier works up to the eighth derivatives (not on the scheme) were used to establish the convergence. Our technique is so general that it can be used to extend the usage of other schemes along the same lines.