A family of fourth order iterative methods for solving nonlinear operator equations

Abstract

In this paper a one parameter family of fourth order methods for the iterative solution of nonlinear operator equations of the form (1) P(x) = 0 where P maps the Banach space X into a Banach space Y, is described. For non-zero values of the parameter, each application of each family member requires no explicit evaluations of derivatives. The convergence of these methods is proved under several assumptions, and a numerical example is given.