Scientific articles

On sets of metric regularity of mappings in spaces with vector-valued metric

E. A. Pluzhnikova^a, T. V. Zhukovskaya^b, Yu. A. Moiseev<sup>a

a</sup> Tambov State University named after G.R. Derzhavin
^b Tambov State Technical University

Abstract: 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.

UDC: 515.124.2 + 517.988.5

Received: 10.04.2018

DOI: 10.20310/1810-0198-2018-23-123-547-554

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