Geodesic
An Implicit Function Theorem for Inclusions Defined by Close Mappings
Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 483-489

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with the question of the solvability of inclusions $F(x,\sigma)\in Q$ for mappings $F$ close, in some metrics, to a given mapping $\widehat{F}$.
Keywords: implicit function, Brouwer's fixed point theorem, Newton's method. 
@article{MZM_2018_103_4_a0,
     author = {E. R. Avakov and G. G. Magaril-Il'yaev},
     title = {An {Implicit} {Function} {Theorem} for {Inclusions} {Defined} by {Close} {Mappings}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--489},
     publisher = {mathdoc},
     volume = {103},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a0/}
}
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E. R. Avakov; G. G. Magaril-Il'yaev. An Implicit Function Theorem for Inclusions Defined by Close Mappings. Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 483-489. http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a0/