Separation of B<sup>-1</sup>-Convex Sets by B<sup>-1</sup>-Measurable Maps

G. Tinaztepe; I. Yesilce; G. Adilov

Geodesic

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Separation of B^-1-Convex Sets by B^-1-Measurable Maps

G. Tinaztepe ; I. Yesilce ; G. Adilov

Journal of convex analysis, Tome 21 (2014) no. 2, pp. 571-58.

Voir la notice de l'article provenant de la source Heldermann Verlag

Résumé

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.

Classification : 52A30, 52A01, 52A41, 26B25
Mots-clés : B-convexity, half spaces, gauges, co-gauges, separation, B-measurable maps

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     author = {G. Tinaztepe and I. Yesilce and G. Adilov},
     title = {Separation of {B\protect\textsuperscript{-1}-Convex} {Sets} by {B\protect\textsuperscript{-1}-Measurable} {Maps}},
     journal = {Journal of convex analysis},
     pages = {571--58},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_2_JCA_2014_21_2_a13/}
}

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G. Tinaztepe; I. Yesilce; G. Adilov. Separation of B^-1-Convex Sets by B^-1-Measurable Maps. Journal of convex analysis, Tome 21 (2014) no. 2, pp. 571-58. http://geodesic.mathdoc.fr/item/JCA_2014_21_2_JCA_2014_21_2_a13/