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. 
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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/

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