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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 304, Pages 205–220
DOI: https://doi.org/10.4213/tm3967 (Mi tm3967) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Criteria for Convexity of Closed Sets in Banach Spaces

Yu. S. Ledyaev

Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008-5248, USA
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DOI: https://doi.org/10.4213/tm3967
Abstract: Criteria for the convexity of closed sets in general Banach spaces in terms of the Clarke and Bouligand tangent cones are proved. In the case of uniformly convex spaces, these convexity criteria are stated in terms of proximal normal cones. These criteria are used to derive sufficient conditions for the convexity of the images of convex sets under nonlinear mappings and multifunctions.
Funding agency Grant number
National Science Foundation DMS-0708019
This work was partially supported by the National Science Foundation grant DMS-0708019.
Received: October 2, 2018
Revised: October 22, 2018
Accepted: January 17, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 304, Pages 190–204
DOI: https://doi.org/10.1134/S0081543819010139
Bibliographic databases:
Document Type: Article
UDC: 517.982.252
Language: Russian
Citation: Yu. S. Ledyaev, “Criteria for Convexity of Closed Sets in Banach Spaces”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 205–220; Proc. Steklov Inst. Math., 304 (2019), 190–204
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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