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

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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. 
@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},
     publisher = {mathdoc},
     volume = {86},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a0/}
}
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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/