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Journal of Convex Analysis 28 (2021), No. 4, [final page numbers not yet available]
Copyright Heldermann Verlag 2021

Proximal Determination of Convex Functions

Emilio Vilches
Instituto de Ciencias de la Ingenierķa, Universidad de O'Higgins, Rancagua, Chile

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.

Keywords: Proximal operator, determination of convex functions, Moreau decomposition, Legendre-Fenchel conjugate.

MSC: 49J52, 46N10.

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