Argyros, I.K.Khattri, S.K.George, S.2026-02-052018Advances in Nonlinear Variational Inequalities, 2018, 21, 2, pp. 1-171092910Xhttps://idr.nitk.ac.in/handle/123456789/25084We expand the applicability of the Halley's method for approximating a locally unique solution of nonlinear equations in a Banach space setting. Our majorizing sequences are finer than in earlier studies such as [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 19, 20, 21, 23] and furthermore developed convergence criteria can be weaker. Finally numerical work is reported that compares favorably to the existing approaches in the literature [6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 24, 25, 26, 28]. © 2018 International Publications. All rights reserved.Banach spaceFréchet-derivativeHalley methodMajorizing sequenceSemilocal convergence