Geodesic
On a property of the Fenchel transform
Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 474-478 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the class of functions $\Phi \colon \mathbb{R} \to [0, + \infty]$, which are lower semicontinuous, even, convex and $ \Phi (0) = 0 $. The Fenchel transform $\Psi$ from $\Phi$ also belongs to this class of functions. We will define functions that play the role of derivatives for all functions from our class and prove that these functions are mutually inverse in a generalized sense.
Keywords: utility maximization, Orlicz space
Mots-clés : Fenchel transform. 
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     title = {On a property of the {Fenchel} transform},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a32/}
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A. A. Farvazova. On a property of the Fenchel transform. Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 474-478. http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a32/

[1] Rao M. M., Ren Z. D., Theory of Orlicz Spaces, Marcel Dekker, N.Y., 1991 | MR | Zbl

[2] Embrechts P., Hofert M., “A note on generalized inverses”, Math. Meth. of Oper. Res., 77:3 (2013), 423–432 | DOI | MR | Zbl

[3] Meyer P.-A., Probability and potentials, Mir, M., 1973