A NEWTON-TYPE METHOD IN K-NORMED SPACES

Abstract

We use our new idea of recurrent functions to provide a new semilocal convergence result for a Newton-type method (NTM) for solving a nonlinear operator equation in a K-normed space setting. Using more precise majorizing sequences than before [3], [8], we show how to expand the convergence domain of (NTM) under the same computational cost as before [3], [8]. A numerical examples shows how to solve an equation in cases not covered before.