Journal of Convex Analysis 21 (2014), No. 2, 571--580
Copyright Heldermann Verlag 2014
Separation of B-1-Convex Sets by B-1-Measurable Maps
Gultekin Tinaztepe
Vocational School of Technical Sciences, Akdeniz University, Dumlupinar Boulevard, 07058 Campus Antalya, Turkey
gtinaztepe@akdeniz.edu.tr
Ilknur Yesilce
Faculty of Science and Letters, Mersin University, Ciftlikkoy Campus, 33343 Mersin, Turkey
ilknuryesilce@gmail.com
Gabil Adilov
Faculty of Education, Akdeniz University, Dumlupinar Boulevard, 07058 Campus Antalya, Turkey
gabiladilov@gmail.com
[Abstract-pdf]
A subset $A$ of $\mathbb{R}^{n}_{++}$ is B$^{-1}$-convex if for all $x_{1},x_{2}\in A$ and all $t\geq1$ one has $tx_{1}\wedge x_{2}\in A$. These sets were first investigated in papers of G. Adilov and I. Yesilce [``B$^{-1}-$convex sets and B$^{-1}-$measurable maps'', Numerical Functional Analysis and Optimization 33(2) (2012) 131--141; ``On Generalization of the Concept of Convexity'', Hacettepe Journal of Mathematics and Statistics 41(5) (2012) 723--730], and of W. Briec and Q. B. Liang [``On Some Semilattice Structures for Production Technologies'', European Journal of Operational Research 215 (2011) 740--749].\par In this paper, we establish separation and a Hahn-Banach-like Theorem for B$^{-1}$-convex sets.
Keywords: B-convexity, half spaces, gauges, co-gauges, separation, B-measurable maps.
MSC: 52A30, 52A01, 52A41, 26B25
[ Fulltext-pdf (139 KB)] for subscribers only.