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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 6, Pages 47–68 (Mi izv941)  

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

Lipschitz continuous parametrizations of set-valued maps with weakly convex images

G. E. Ivanov, M. V. Balashov

Moscow Institute of Physics and Technology

Abstract: We continue the investigations started in [1]–[4], where weakly convex sets and set-valued maps with weakly convex images were studied. Sufficient conditions are found for the existence of a Lipschitz parametrization for a set-valued map with solidly smooth (generally, non-convex) images. It is also shown that the set-valued $\varepsilon$-projection on a weakly convex set and the unit outer normal vector to a solidly smooth set satisfy, as set functions, the Lipschitz condition and the Hölder condition with exponent $1/2$, respectively, relative to the Hausdorff metric.

DOI: https://doi.org/10.4213/im941

Full text: PDF file (606 kB)
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English version:
Izvestiya: Mathematics, 2007, 71:6, 1123–1143

Bibliographic databases:

UDC: 517.982.252, 517.982.256
MSC: 26B05, 26B25, 26E15, 26E25, 28B20, 34A12, 34A60, 34D20, 46G05, 47H04, 47H10, 49J15, 49J45, 49J52, 49K15, 49M37, 49N70, 49N75, 52A01, 52A20, 52A27, 54C30, 54C60, 90C30, 91A23, 93B03, 93B15, 34-02, 47Hxx, 49-02
Received: 15.03.2006

Citation: G. E. Ivanov, M. V. Balashov, “Lipschitz continuous parametrizations of set-valued maps with weakly convex images”, Izv. RAN. Ser. Mat., 71:6 (2007), 47–68; Izv. Math., 71:6 (2007), 1123–1143

Citation in format AMSBIB
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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. Balashov M. V., Repovš D., “On the splitting problem for selections”, J. Math. Anal. Appl., 355:1 (2009), 277–287  crossref  mathscinet  zmath  isi  elib  scopus
    2. I. G. Tsarkov, “Ustoichivost otnositelnogo chebyshëvskogo proektora v poliedralnykh prostranstvakh”, Tr. IMM UrO RAN, 24, no. 4, 2018, 235–245  mathnet  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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