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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
