Ball convergence of Newton's method for generalized equations using restricted convergence domains and majorant conditions

Abstract

In this study, we consider Newton's method for solving the generalized equation of the form F(x) + T(x) ? 0; in Hilbert space, where F is a Fr chet differentiable operator and T is a set valued and maximal monotone. Using restricted convergence domains and Banach Perturbation lemma 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 but using more precise majorant functions. 2017 Kyungnam University Press.