Separation of B-1-Convex Sets by B-1-Measurable Maps
JOURNAL OF CONVEX ANALYSIS, vol.21, no.2, pp.571-580, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 21 Issue: 2
- Publication Date: 2014
- Journal Name: JOURNAL OF CONVEX ANALYSIS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.571-580
- Keywords: B-convexity, B-1-convexity, half spaces, gauges, co-gauges, separation, B-1-measurable maps, B-CONVEXITY
- Akdeniz University Affiliated: Yes
Abstract
A subset A of R-++(n) is B-1-convex if for all x(1), x(2) epsilon A and all t >= 1 one has tx(1) Lambda x(2) epsilon A. These sets were first investigated in [2, 3, 7]. In this paper, we establish separation and Hahn-Banach like Theorem for B-1-convex sets.