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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
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.
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
Linking options:
https://www.mathnet.ru/eng/tm3967https://doi.org/10.4213/tm3967 https://www.mathnet.ru/eng/tm/v304/p205
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Abstract page: | 271 | Full-text PDF : | 86 | References: | 42 | First page: | 21 |
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