Geodesic
On a property of the Fenchel transform
Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 474-478

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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, Fenchel transform. 
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     author = {A. A. Farvazova},
     title = {On a property of the {Fenchel} transform},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {474--478},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2021},
     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/