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Mat. Zametki, 1996, Volume 60, Issue 3, Pages 406–413 (Mi mz1840)  

This article is cited in 4 scientific papers (total in 4 papers)

Partial convexity

N. N. Metel'skii, V. N. Martynchik

Institute of Mathematics, National Academy of Sciences of the Republic of Belarus

Abstract: We consider a generalization of the classical notion of convexity, which is called partial convexity. Let $V\subseteq\mathbb R^n$ be some set of directions. A set $X\subseteq\mathbb R^n$ is called $V$-convex if the intersection of any line parallel to a vector in $V$ with $X$ is connected. Semispaces and the problem of the least intersection base for partial convexity is investigated. The cone of convexity directions is described for a closed set in $\mathbb R^n$.

DOI: https://doi.org/10.4213/mzm1840

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English version:
Mathematical Notes, 1996, 60:3, 300–305

Bibliographic databases:

UDC: 514.17+519.85
Received: 20.03.1995

Citation: N. N. Metel'skii, V. N. Martynchik, “Partial convexity”, Mat. Zametki, 60:3 (1996), 406–413; Math. Notes, 60:3 (1996), 300–305

Citation in format AMSBIB
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\by N.~N.~Metel'skii, V.~N.~Martynchik
\paper Partial convexity
\jour Mat. Zametki
\yr 1996
\vol 60
\issue 3
\pages 406--413
\mathnet{http://mi.mathnet.ru/mz1840}
\crossref{https://doi.org/10.4213/mzm1840}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1428854}
\zmath{https://zbmath.org/?q=an:0909.52001}
\transl
\jour Math. Notes
\yr 1996
\vol 60
\issue 3
\pages 300--305
\crossref{https://doi.org/10.1007/BF02320367}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WN90400008}


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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. D. Wood, V. N. Martynchik, N. N. Metel'skii, “Calculation of partially convex hulls and approximations for finite planar sets”, Comput. Math. Math. Phys., 38:8 (1998), 1347–1357  mathnet  mathscinet  zmath
    2. Izobov, NA, “The existence of a linear Pfaff system with disconnected lower characteristic set of positive measure”, Differential Equations, 35:1 (1999), 64  mathnet  mathscinet  zmath  isi
    3. N. N. Metel'skii, V. G. Naidenko, “Algorithmic aspects of partial convexity”, Math. Notes, 68:3 (2000), 345–354  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Naidenko, V, “Optimization on directionally convex sets”, Central European Journal of Operations Research, 17:1 (2009), 55  crossref  mathscinet  zmath  isi  scopus  scopus
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