Argyros, I.K.George, S.2026-02-052019Communications on Applied Nonlinear Analysis, 2019, 26, 2, pp. 92-1021074133Xhttps://idr.nitk.ac.in/handle/123456789/24617We extend the applicability of Newton’s method used to approximate a solution of a mapping involving Lie valued operators. Using our idea of the restricted convergence region, we locate a more precise set containing the Newton iterates leading to tighter majorizing sequences than before. This way and under the same computational cost as before, we show the semi-local convergence of Newton’s method with the following advantages over earlier works: weaker sufficient convergence criteria, tighter error bounds on the distances involved and at least as precise information on the location of the solution. © 2019, International Publications. All rights reserved.Kantorovich hypothesisLie algebraLie groupMajorizing sequenceNewton’s methodRiemannian manifoldSemi-local convergence