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Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 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)

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.

Full text: PDF file (730 kB)
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UDC: 514.17
Received: 18.12.2012

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  elib
    2. 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  mathnet  crossref  crossref  isi  elib
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