Geodesic
Existence and properties of inverse mappings
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 18-28

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Nonlinear mappings in Banach spaces are considered. The covering property, metric regularity, and the existence of a continuous right inverse are considered for these mappings under various assumptions of smoothness. Several regularity conditions that guarantee the local covering property and the existence of a continuous right inverse are presented. 
@article{TM_2010_271_a2,
     author = {A. V. Arutyunov and S. E. Zhukovskiy},
     title = {Existence and properties of inverse mappings},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     publisher = {mathdoc},
     volume = {271},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_271_a2/}
}
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A. V. Arutyunov; S. E. Zhukovskiy. Existence and properties of inverse mappings. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 18-28. http://geodesic.mathdoc.fr/item/TM_2010_271_a2/