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This article is cited in 17 scientific papers (total in 17 papers)
Weak convexity in the senses of Vial and Efimov–Stechkin
G. E. Ivanov
Abstract:
Research in convex analysis (in particular, in the theory of strongly convex sets developed in recent years) has made it possible to obtain important results in approximation theory, the theory of extremal problems, optimal control and differential game theory [1]–[3]. In many problems there arise non-convex sets that have weakened convexity properties, which enables one to study them using the methods of convex analysis. In this paper we study new properties of sets that are weakly convex in the sense of Vial or Efimov–Stechkin, that is, in the direct and dual senses. We establish relations between these two concepts of weak convexity. For subsets of Hilbert space that are weakly convex in the sense of Vial we prove a theorem on relative connectedness and a support principle.
Received: 07.09.2004
Citation:
G. E. Ivanov, “Weak convexity in the senses of Vial and Efimov–Stechkin”, Izv. RAN. Ser. Mat., 69:6 (2005), 35–60; Izv. Math., 69:6 (2005), 1113–1135
Linking options:
https://www.mathnet.ru/eng/im665https://doi.org/10.1070/IM2005v069n06ABEH002292 https://www.mathnet.ru/eng/im/v69/i6/p35
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Abstract page: | 546 | Russian version PDF: | 217 | English version PDF: | 41 | References: | 50 | First page: | 1 |
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