IMPROVED ROBUST SEMI-LOCAL CONVERGENCE ANALYSIS OF NEWTON’S METHOD FOR CONE INCLUSION PROBLEM IN BANACH SPACES UNDER RESTRICTED CONVERGENCE DOMAINS AND MAJORANT CONDITIONS

Abstract

In this study, we consider Newton’s method for solving the nonlinear inclusion problems in Banach space, where F is a Fr ́echet differentiable operator. Using restricted convergence domains we prove the convergence of the method with the following advantages: tighter error estimates on the distances involved and the information on the location of the solution is at least as precise. These advantages were obtained under the same computational cost using the idea of restricted convergence domains.