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Journal of Convex Analysis 15 (2008), No. 2, 285--297
Copyright Heldermann Verlag 2008



Comparing Fenchel-Moreau Conjugates with Level Set Conjugates

Juan-Enrique MartŪnez-Legaz
Dep. d'Economia i d'HistÚria EconÚmica, Universitat AutÚnoma 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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