Broadening the convergence domain of Seventh-order method satisfying Lipschitz and Hölder conditions

Abstract

The local convergence analysis of a seventh order algorithm for solving nonlinear equations is presented in the current discussion by assuming that the rst-order Fréchet derivative belongs to the Lipschitz class. This approach yields radii of convergence ball, error bound and uniqueness of the solution. Further, generalization of the study extended by considering Hölder continuity condition. At last, we estimated the radii of the convergence balls using a variety of numerical examples, including a nonlinear Hammerstein equation.