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Izv. Akad. Nauk SSSR Ser. Mat., 1962, Volume 26, Issue 1, Pages 87–106 (Mi izv3188)  

This article is cited in 22 scientific papers (total in 22 papers)

On the optimal net and best cross-section of a set in a normed space

A. L. Garkavi


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Received: 14.03.1960

Citation: A. L. Garkavi, “On the optimal net and best cross-section of a set in a normed space”, Izv. Akad. Nauk SSSR Ser. Mat., 26:1 (1962), 87–106

Citation in format AMSBIB
\Bibitem{Gar62}
\by A.~L.~Garkavi
\paper On the optimal net and best cross-section of a~set in a~normed space
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1962
\vol 26
\issue 1
\pages 87--106
\mathnet{http://mi.mathnet.ru/izv3188}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=136969}
\zmath{https://zbmath.org/?q=an:0158.13602|0108.10801}


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

    This publication is cited in the following articles:
    1. V. D. Milman, “Geometric theory of Banach spaces. Part II. Geometry of the unit sphere”, Russian Math. Surveys, 26:6 (1971), 79–163  mathnet  crossref  mathscinet  zmath
    2. A. L. Garkavi, V. A. Shmatkov, “On the Lamé point and its generalizations in a normed space”, Math. USSR-Sb., 24:2 (1974), 267–286  mathnet  crossref  mathscinet  zmath
    3. I. G. Tsar'kov, “Smoothing of uniformly continuous mappings in $L_p$ spaces”, Math. Notes, 54:3 (1993), 957–967  mathnet  crossref  mathscinet  zmath  isi
    4. I. G. Tsar'kov, “Polynomial Approximation of Vector Functions”, Funct. Anal. Appl., 29:3 (1995), 222–223  mathnet  crossref  mathscinet  zmath  isi
    5. P. V. Semenov, “Fixed-point theorems for a controlled withdrawal of the convexity of the values of a set-valued map”, Sb. Math., 189:3 (1998), 461–480  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. E. N. Sosov, “The best net, the best section, and the Chebyshev center of a bounded set in an infinite-dimensional Lobachevskii space”, Russian Math. (Iz. VUZ), 43:9 (1999), 39–43  mathnet  mathscinet  zmath  elib
    7. E. N. Sosov, “On the $\varepsilon$-core of a bounded set in a special metric space”, Russian Math. (Iz. VUZ), 44:9 (2000), 32–35  mathnet  mathscinet  zmath  elib
    8. E. N. Sosov, “On the best $N$-nets of bounded closed convex sets in a special metric space”, Russian Math. (Iz. VUZ), 47:9 (2003), 39–42  mathnet  mathscinet  zmath  elib
    9. E. N. Sosov, “The relative Chebyshev center of a finite set in a geodesic space”, Russian Math. (Iz. VUZ), 52:4 (2008), 59–64  mathnet  crossref  mathscinet  zmath  elib
    10. E. N. Sosov, “Metricheskoe prostranstvo vsekh $N$-setei geodezicheskogo prostranstva”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 151, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2009, 136–149  mathnet  elib
    11. E. N. Sosov, “Sufficient conditions for existence and uniqueness of a Chebyshev center of a nonempty bounded set in a geodesic space”, Russian Math. (Iz. VUZ), 54:6 (2010), 39–42  mathnet  crossref  mathscinet  elib
    12. E. N. Sosov, “Otnositelnyi $N$-radius ogranichennogo mnozhestva metricheskogo prostranstva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 153, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2011, 28–36  mathnet
    13. P. D. Lebedev, A. V. Ushakov, “Approximating sets on a plane with optimal sets of circles”, Autom. Remote Control, 73:3 (2012), 485–493  mathnet  crossref  isi
    14. P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Algoritmy nailuchshei approksimatsii ploskikh mnozhestv ob'edineniyami krugov”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 4, 88–99  mathnet
    15. P. D. Lebedev, D. S. Bukharov, “Approksimatsiya mnogougolnikov nailuchshimi naborami krugov”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:3 (2013), 72–87  mathnet
    16. V. N. Ushakov, A. S. Lakhtin, P. D. Lebedev, “Optimization of the Hausdorff distance between sets in Euclidean space”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 222–238  mathnet  crossref  mathscinet  isi  elib
    17. V. N. Ushakov, P. D. Lebedev, “Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 225–237  mathnet  crossref  mathscinet  isi  elib
    18. V. N. Ushakov, P. D. Lebedev, “Algoritmy optimalnogo pokrytiya mnozhestv na ploskosti $\mathbb{R}^2$”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:2 (2016), 258–270  mathnet  crossref  mathscinet  elib
    19. A. L. Kazakov, P. D. Lebedev, “Algorithms for constructing optimal $n$-networks in metric spaces”, Autom. Remote Control, 78:7 (2017), 1290–1301  mathnet  crossref  mathscinet  isi  elib
    20. P. D. Lebedev, N. G. Lavrov, “Algoritmy postroeniya optimalnykh upakovok sharov v ellipsoidy”, Izv. IMI UdGU, 52 (2018), 59–74  mathnet  crossref  elib
    21. P. D. Lebedev, “Iteratsionnye metody postroeniya approksimatsii optimalnykh pokrytii nevypuklykh ploskikh mnozhestv”, Chelyab. fiz.-matem. zhurn., 4:1 (2019), 5–17  mathnet  crossref  elib
    22. A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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