Regmi, S.Argyros, I.K.George, S.Argyros, C.I.2026-02-042023Contemporary Mathematics (Singapore), 2023, 4, 1, pp. -27051064https://doi.org/10.37256/cm.4120232070https://idr.nitk.ac.in/handle/123456789/22181The application of the Chebyshev-Halley type scheme for nonlinear equations is extended with no additional conditions. In particular, the purpose of this study is two folds. The proof of the semi-local convergence analysis is based on the recurrence relation technique in the first fold. In the second fold, the proof relies on majorizing sequences. Iterates are shown to belong to a larger domain resulting in tighter Lipschitz constants and a finer convergence analysis than in earlier works. The convergence order of these methods is at least three. The numerical example further validates the theoretical results. © 2023 Samundra Regmi, et al.Banach spaceChebyshev-Halley-like schemeconvergence