Geodesic
Stability of Coincidence Points and Properties of Covering Mappings
Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 163-169

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

Properties of closed set-valued covering mappings acting from one metric space into another are studied. Under quite general assumptions, it is proved that, if a given $\alpha$-covering mapping and a mapping satisfying the Lipschitz condition with constant $\beta<\alpha$ have a coincidence point, then this point is stable under small perturbations (with respect to the Hausdorff metric) of these mappings. This assertion is meaningful for single-valued mappings as well. The structure of the set of coincidence points of an $\alpha$-covering and a Lipschitzian mapping is studied. Conditions are obtained under which the limit of a sequence of $\alpha$-covering set-valued mappings is an $(\alpha-\varepsilon)$-covering for an arbitrary $\varepsilon>0$.
Keywords: coincidence point, set-valued mapping, covering mapping, metric space, Lipschitzian mapping, generalized Hausdorff metric, complete space. 
A. V. Arutyunov. Stability of Coincidence Points and Properties of Covering Mappings. Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 163-169. http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a0/
@article{MZM_2009_86_2_a0,
     author = {A. V. Arutyunov},
     title = {Stability of {Coincidence} {Points} and {Properties} of {Covering} {Mappings}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--169},
     year = {2009},
     volume = {86},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a0/}
}
TY  - JOUR
AU  - A. V. Arutyunov
TI  - Stability of Coincidence Points and Properties of Covering Mappings
JO  - Matematičeskie zametki
PY  - 2009
SP  - 163
EP  - 169
VL  - 86
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a0/
LA  - ru
ID  - MZM_2009_86_2_a0
ER  - 
%0 Journal Article
%A A. V. Arutyunov
%T Stability of Coincidence Points and Properties of Covering Mappings
%J Matematičeskie zametki
%D 2009
%P 163-169
%V 86
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a0/
%G ru
%F MZM_2009_86_2_a0

[1] Dzh. L. Kelli, Obschaya topologiya, Nauka, M., 1981 | MR | Zbl

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

[3] A. D. Ioffe, “Metricheskaya regulyarnost i subdifferentsialnoe ischislenie”, UMN, 55:3 (2000), 103–162 | MR | Zbl

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