Geodesic
Regular smoothness and the Newton--Kantorovich method
Trudy Instituta matematiki, Tome 19 (2011) no. 1, pp. 52-61.

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The article deals with the Newton–Kantorovich method for solving nonlinear operator equations under the regular smoothness assumption. The main convergence theorem is proved by means of the majorant method of Kantorovich. 
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P. P. Zabreiko; A. N. Tanyhina. Regular smoothness and the Newton--Kantorovich method. Trudy Instituta matematiki, Tome 19 (2011) no. 1, pp. 52-61. http://geodesic.mathdoc.fr/item/TIMB_2011_19_1_a5/

[1] Galperin A., Waksman Z., “Newton's method under a weak smoothness assumption”, J. Comp. Appl. Math., 35 (1991), 207–215 | DOI | MR | Zbl

[2] Galperin A., Waksman Z., “Regular smoothness and Newton's method”, Numer. Funct. Anal. and Optimiz., 15:78 (1994), 813–858 | DOI | MR | Zbl

[3] Zabrejko P.P., Nguen D.F., “The majorant method in the theory of Newton–Kantorovich approximations and the Pták error estimates”, Numer. Funct. Anal. and Optimiz., 9:56 (1987), 671–684 | DOI | MR | Zbl