Geodesic
Proximal Determination of Convex Functions
Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1187-1192
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We provide comparison principles for convex functions through its proximal mappings. Consequently, we prove that the norm of the proximal operator determines a convex the function up to a constant. A new characterization of Lipschitzianity in terms of the proximal operator is given.
Classification : 49J52, 46N10
Mots-clés : Proximal operator, determination of convex functions, Moreau decomposition, Legendre-Fenchel conjugate 
@article{JCA_2021_28_4_JCA_2021_28_4_a10,
     author = {E. Vilches},
     title = {Proximal {Determination} of {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {1187--1192},
     year = {2021},
     volume = {28},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a10/}
}
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E. Vilches. Proximal Determination of Convex Functions. Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1187-1192. http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a10/