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Mat. Sb., 2007, Volume 198, Number 1, Pages 43–58 (Mi msb1479)  

This article is cited in 9 scientific papers (total in 9 papers)

Relations between several problems of estimating convex compacta by balls

S. I. Dudov

Saratov State University named after N. G. Chernyshevsky

Abstract: Finite-dimensional problems of finding outer, inner, and uniform estimates for a convex compactum by a ball in an arbitrary norm are considered and compared, as well as the problem of finding estimates of the boundary of a convex compactum by a spherical annulus of the smallest width. It is shown that these problems can be linked by means of the parametric problem of finding the best approximation in the Hausdorff metric of the compactum under consideration by a ball of fixed radius. One can indicate ranges of the fixed radius in which solutions of the latter problem give solutions of the problems mentioned above. However, for some values of the radius this latter problem can be independent.
Bibliography: 12 titles.

DOI: https://doi.org/10.4213/sm1479

Full text: PDF file (511 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:1, 39–53

Bibliographic databases:

UDC: 519.853.3
MSC: Primary 52A27; Secondary 90C90
Received: 15.12.2005

Citation: S. I. Dudov, “Relations between several problems of estimating convex compacta by balls”, Mat. Sb., 198:1 (2007), 43–58; Sb. Math., 198:1 (2007), 39–53

Citation in format AMSBIB
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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. S. I. Dudov, A. S. Dudova, “On the stability of inner and outer approximations of a convex compact set by a ball”, Comput. Math. Math. Phys., 47:10 (2007), 1589–1602  mathnet  crossref  mathscinet  elib  elib
    2. S. I. Dudov, E. V. Sorina, “Uniform estimation of a segment function by a polynomial strip of fixed width”, Comput. Math. Math. Phys., 51:11 (2011), 1864–1877  mathnet  crossref  isi
    3. S. I. Dudov, E. A. Meshcheryakova, “Method for finding an approximate solution of the asphericity problem for a convex body”, Comput. Math. Math. Phys., 53:10 (2013), 1483–1493  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. S. I. Dudov, M. A. Osiptsev, “O podkhode k priblizhennomu resheniyu zadachi nailuchshego priblizheniya vypuklogo tela sharom fiksirovannogo radiusa”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:3 (2014), 267–272  mathnet  crossref  elib
    5. S. I. Dudov, E. A. Meshcheryakova, “On asphericity of convex body”, Russian Math. (Iz. VUZ), 59:2 (2015), 36–47  mathnet  crossref
    6. Sergey Dudov, Mikhail Osiptsev, “Uniform Estimation of a Convex Body by a Fixed-Radius Ball”, J Optim Theory Appl, 2015  crossref  mathscinet  scopus
    7. S. I. Dudov, “Systematization of problems on ball estimates of a convex compactum”, Sb. Math., 206:9 (2015), 1260–1280  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. S. I. Dudov, M. A. Osiptsev, “Ob ustoichivosti po funktsionalu resheniya zadachi o nailuchshem priblizhenii vypuklogo tela sharom fiksirovannogo radiusa”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:3 (2015), 273–279  mathnet  crossref  elib
    9. S. I. Dudov, M. A. Osiptsev, “Stability of best approximation of a convex body by a ball of fixed radius”, Comput. Math. Math. Phys., 56:4 (2016), 525–540  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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