Geodesic
On sets of metric regularity of mappings in spaces with vector-valued metric
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 547-554

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Spaces with vector-valued metric are considered. The values of a vectorvalued metric are elements of a cone in some linear normed space. The concept of the set of metric regularity for mapping in spaces with vector-valued metric is formulated. A statement on the stability of the set of metric regularity of a given mapping for its Lipschitz perturbations in spaces with vector-valued metric is obtained.
Keywords: nonlinear mapping, space with vector-valued metric, the set of metric Regularity. 
@article{VTAMU_2018_23_123_a25,
     author = {E. A. Pluzhnikova and T. V. Zhukovskaya and Yu. A. Moiseev},
     title = {On sets of metric regularity of mappings in spaces with vector-valued metric},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {547--554},
     publisher = {mathdoc},
     volume = {23},
     number = {123},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a25/}
}
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E. A. Pluzhnikova; T. V. Zhukovskaya; Yu. A. Moiseev. On sets of metric regularity of mappings in spaces with vector-valued metric. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 547-554. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a25/