Geodesic
General Implicit Function Theorem for Close Mappings
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 7-18

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We prove a sufficiently general implicit function theorem for mappings that are close to an original one in the uniform metric of the space of continuous mappings. As a corollary, we derive an important (for applications) result related to perturbations of linear mappings.
Keywords: implicit function, close mappings, metric regularity. 
@article{TM_2021_315_a0,
     author = {E. R. Avakov and G. G. Magaril-Il'yaev},
     title = {General {Implicit} {Function} {Theorem} for {Close} {Mappings}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {7--18},
     publisher = {mathdoc},
     volume = {315},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_315_a0/}
}
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E. R. Avakov; G. G. Magaril-Il'yaev. General Implicit Function Theorem for Close Mappings. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 7-18. http://geodesic.mathdoc.fr/item/TM_2021_315_a0/