Geodesic
On the continuity of inverse mappings for Lipschitz perturbations of covering mappings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 4, pp. 93-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study the question of the existence of a continuous right inverse mapping for a covering mapping. To describe covering mappings that have a continuous right inverse, a concept of strong covering is introduced. It is shown that the property of strong covering is stable under small Lipschitz perturbations. 
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A. V. Arutyunov; S. E. Zhukovskiy. On the continuity of inverse mappings for Lipschitz perturbations of covering mappings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 4, pp. 93-99. http://geodesic.mathdoc.fr/item/FPM_2014_19_4_a2/

[1] Arutyunov A. V., “Teorema o neyavnoi funktsii bez apriornykh predpolozhenii normalnosti”, Zh. vychisl. matem. i matem. fiz., 46:2 (2006), 205–215 | MR | Zbl

[2] Arutyunov A. V., “Nakryvayuschie otobrazheniya v metricheskikh prostranstvakh i nepodvizhnye tochki”, Dokl. RAN, 416:2 (2007), 151–155 | MR | Zbl

[3] Arutyunov A. V., “Ustoichivost tochek sovpadeniya i svoistva nakryvayuschikh otobrazhenii”, Matem. zametki, 86:2 (2009), 163–169 | DOI | MR | Zbl

[4] Arutyunov A. V., “Zadacha o tochkakh sovpadeniya mnogoznachnykh otobrazhenii i ustoichivost po Ulamu–Khaiersu”, Dokl. RAN, 455:4 (2014), 379–383 | DOI | MR | Zbl

[5] Arutyunov A. V., Avakov E. R., Zhukovskii E. S., “Nakryvayuschie otobrazheniya i ikh prilozheniya k differentsialnym uravneniyam, ne razreshënnym otnositelno proizvodnoi”, Differents. uravn., 45:5 (2009), 613–634 | MR | Zbl

[6] Arutyunov A. V., Zhukovskii E. S., Zhukovskii S. E., “O korrektnosti differentsialnykh uravnenii, ne razreshënnykh otnositelno proizvodnoi”, Differents. uravn., 47:11 (2011), 1523–1537 | MR | Zbl

[7] Arutyunov A. V., Zhukovskii S. E., “Lokalnaya razreshimost upravlyaemykh sistem so smeshannymi ogranicheniyami”, Differents. uravn., 46:11 (2010), 1561–1570 | MR | Zbl

[8] Arutyunov A. V., Zhukovskii S. E., “Suschestvovanie obratnykh otobrazhenii i ikh svoistva”, Tr. Mat. In-ta im. V. A. Steklova, 271, 2010, 18–28 | MR | Zbl

[9] Dmitruk A. V., Milyutin A. A., Osmolovskii N. P., “Teorema Lyusternika i teoriya ekstremuma”, UMN, 35:6(216) (1980), 11–46 | MR | Zbl

[10] Tikhomirov V. M., “Teorema Lyusternika o kasatelnom prostranstve i nekotorye eë modifikatsii”, Optimalnoe upravlenie, Matem. vopr. upravleniya proizvodstvom, 7, 1977, 22–30

[11] Arutyunov A., Avakov E., Gel'man B., Dmitruk A., Obukhovskii V., “Locally covering maps in metric spaces and coincidence points”, J. Fixed Points Theory and Appl., 5:1 (2009), 105–127 | DOI | MR | Zbl

[12] Arutyunov A. V., Zhukovskiy E. S., Zhukovskiy S. E., “Covering mappings and well-posedness of nonlinear Volterra equations”, Nonlinear Anal., 75:3 (2012), 1026–1044 | DOI | MR | Zbl

[13] Dontchev A. L., Rockafellar R.T., Implicit Functions and Solution Mappings, Springer Monographs Math., Springer, Berlin, 2009 | DOI | MR | Zbl

[14] Graves L. M., “Some mapping theorems”, Duke Math. J., 17 (1950), 111–114 | DOI | MR | Zbl

[15] Mordukhovich B. Sh., “Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions”, Trans. Amer. Math. Soc., 340 (1993), 1–35 | DOI | MR | Zbl

[16] Mordukhovich B. S., Variational Analysis and Generalized Differentiation, v. I, Basic Theory, Springer, Berlin, 2006 | MR

[17] Uderzo A., “A metric version of Milyutin theorem”, Set-Valued Var. Anal., 20:2 (2012), 279–306 | DOI | MR | Zbl