Geodesic
A convergence theorem for the Newton method
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 242-246

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The convergence of the Newton method is established dor equations of the form $Tx+F(x)=0$, where $T$ is an unbounded operator, and the Fréchet derivative $F'(u)$ of the operator $F(u)$ satisfies Hölder's condition. 
@article{ZNSL_1998_248_a13,
     author = {M. N. Yakovlev},
     title = {A convergence theorem for the {Newton} method},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {242--246},
     publisher = {mathdoc},
     volume = {248},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a13/}
}
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M. N. Yakovlev. A convergence theorem for the Newton method. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 242-246. http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a13/