Geodesic
On the approximate construction of an implicit function
Sbornik. Mathematics, Tome 40 (1981) no. 3, pp. 429-433

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The author considers an iterative projection method of constructing an implicit function under conditions that are satisfied in the standard implicit function theorem. It is shown that the method is applicable for finding solutions of equations under conditions analogous to those of the Newton–Kantorovich method. Bibliography: 7 titles. 
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     author = {A. A. Fonarev},
     title = {On the approximate construction of an implicit function},
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A. A. Fonarev. On the approximate construction of an implicit function. Sbornik. Mathematics, Tome 40 (1981) no. 3, pp. 429-433. http://geodesic.mathdoc.fr/item/SM_1981_40_3_a6/