Journal of Convex Analysis 15 (2008), No. 2, 285--297
Copyright Heldermann Verlag 2008
Comparing Fenchel-Moreau Conjugates with Level Set Conjugates
Juan-Enrique Martínez-Legaz
Dep. d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
Ivan Singer
Institute of Mathematics, P.O. Box 1-764, 70700 Bucharest, Romania
[Abstract-pdf]
We compare the Fenchel-Moreau second conjugates associated to an arbitrary coupling function $\varphi :X\times W\rightarrow \overline{R}=[-\infty ,+\infty ]$ between two sets $X$ and $W$ with the second level set conjugates associated to the same coupling. For a coupling $\varphi :R^{n}\times R^{n}\rightarrow R=(-\infty ,+\infty )$ that is additively homogeneous in one (or both) of the variables we also compare the first conjugates associated to the same coupling. We give an application to the ``min-type'' coupling function arising in the study of topical functions.
Keywords: Generalized conjugation, topical functions, hull operators.
MSC: 49N15, 26B25, 52A01.
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