On a property of the Fenchel transform
https://doi.org/10.22405/2226-8383-2018-22-3-474-478
Abstract
We consider the class of functions Φ: R → [0,+∞], which are lower semicontinuous, even, convex and Φ(0) = 0. The Fenchel transform Ψ from Φ 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.
About the Author
Aisylu Azatovna Farvazova
Lomonosov Moscow State University
Russian Federation
Russian Federation
graduate student
References
1. Rao, M. M. & Ren, Z. D., 1991, Theory of Orlicz Spaces, Marcel Dekker, New-York.
2. Embrechts, P. & Hofert, M., 2013, “A note on generalized inverses”, Math. Meth. of Oper. Res.,
3. vol. 77, no. 3, pp. 423-432.
4. Meyer, P.-A., 1973, Veroyatnost i potentcialy [Probability and potentials], Mir, Moscow.
Review
For citations:
Farvazova A.A. On a property of the Fenchel transform. Chebyshevskii Sbornik. 2021;22(3):474-478. (In Russ.) https://doi.org/10.22405/2226-8383-2018-22-3-474-478
Views:
326
Email this article 