P. D. Lebedev, V. N. Ushakov, “A variant of a metric for unbounded convex sets”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 5:1 (2013), 40

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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika"

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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika", 2013, Volume 5, Issue 1, Pages 40–49 (Mi vyurm47)

This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

A variant of a metric for unbounded convex sets

P. D. Lebedev, V. N. Ushakov

Institute of Mathematics and Mechanics of the Russian Academy of Sciences (Ural branch)

Full-text PDF (730 kB) Citations (2)

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Abstract: Convex analysis methods are used for the construction of distance function between closed (unbounded in common case) sets of Euclidean space. It is shown that the distance satisfies all properties of metric. It is proved that this distance is invariant under motion of the sets in space. This metric space is proved to be complete.

Keywords: Hausdorff distance, metric, convex set, recessive cone.

Received: 18.12.2012

Document Type: Article

UDC: 514.17

Language: Russian

Citation: P. D. Lebedev, V. N. Ushakov, “A variant of a metric for unbounded convex sets”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 5:1 (2013), 40–49

Citation in format AMSBIB

\Bibitem{LebUsh13}

\by P.~D.~Lebedev, V.~N.~Ushakov

\paper A variant of a metric for unbounded convex sets

\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.

\yr 2013

\vol 5

\issue 1

\pages 40--49

\mathnet{http://mi.mathnet.ru/vyurm47}

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https://www.mathnet.ru/eng/vyurm47

https://www.mathnet.ru/eng/vyurm/v5/i1/p40

This publication is cited in the following 2 articles:

E. A. Panasenko, “On the Metric Space of Closed Subsets of a Metric Space and Set-Valued Maps with Closed Images”, Math. Notes, 104:1 (2018), 96–110
V. N. Ushakov, P. D. Lebedev, “Iteratsionnye metody minimizatsii khausdorfova rasstoyaniya mezhdu podvizhnymi mnogougolnikami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:1 (2017), 86–97

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	73

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