Abstract
We provide local convergence results for Halley’s method in order to approximate a locally unique zero of an operator in a Banach space setting using convex majorants. Kantorovich-type and Smale-type results are considered as applications and special cases.
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Argyros, I.K., Ren, H. Ball convergence theorems for Halley’s method in Banach space. J. Appl. Math. Comput. 38, 453–465 (2012). https://doi.org/10.1007/s12190-011-0490-3
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DOI: https://doi.org/10.1007/s12190-011-0490-3