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2018•Tambov University Reports Series Natural and Technical SciencesOpen access

ON SETS OF METRIC REGULARITY OF MAPPINGS IN SPACES WITH VECTOR-VALUED METRIC

Е. А. Плужникова, T. V. Zhukovskaya, Yuriy Anatol’evich Moiseev

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Mathematics, Injective metric space, Metric space, Convex metric space, Metric differential, Metric map, Intrinsic metric, Equivalence of metrics

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