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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     author = {P. P. Zabreiko and A. N. Tanyhina},
     title = {Regular smoothness and the {Newton--Kantorovich} method},
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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/