Scientific articles

The set of regularity of a multivalued mappingin a space with a vector-valued metric

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

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

Abstract: We consider multivalued mappings acting in spaces with a vector-valued metric. A vector-valued metric is understood as a mapping satisfying the axioms “of an ordinary metric” with values in the cone of a linear normed space. The concept of the regularity set of a multivalued mapping is defined. A set of regularity is used in the study of inclusions in spaces with a vector-valued metric.

Keywords: multi-valued mapping; space with vector-valued metric; metric regularity; Lipschitz mapping; inclusion.

UDC: 515.124.2, 515.126.4, 517.988.52

Received: 16.01.2019

DOI: 10.20310/1810-0198-2019-24-125-39-46

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