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Trudy Mat. Inst. Steklova, 2019, Volume 304, Pages 205–220 (Mi tm3967)  

Criteria for Convexity of Closed Sets in Banach Spaces

Yu. S. Ledyaev

Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008-5248, USA

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.


DOI: https://doi.org/10.4213/tm3967

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 304, 190–204

Bibliographic databases:

UDC: 517.982.252
Received: October 2, 2018
Revised: October 22, 2018
Accepted: January 17, 2019

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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\paper Criteria for Convexity of Closed Sets in Banach Spaces
\inbook Optimal control and differential equations
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
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\vol 304
\pages 205--220
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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