On the Rockafellar theorem for $Φ^{γ(·,·)}$-monotone multifunctions

S. Rolewicz

On the Rockafellar theorem for

Φ^{γ (\cdot, \cdot)}

-monotone multifunctions

S. Rolewicz

Studia Mathematica, Tome 173 (2006), p. 197-202 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let $Γ : X \to 2^{Φ}$ be a cyclic $Φ^{γ (\cdot, \cdot)}$ -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the $Φ^{γ (\cdot, \cdot)}$ -subdifferential of f, $Γ (x) \subset \partial_{Φ}^{γ (\cdot, \cdot)} {f |}_{x}$ .

Publié le : 2006-01-01

Zbl 1099.46050

EUDML-ID : urn:eudml:doc:284965

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S. Rolewicz. On the Rockafellar theorem for $Φ^{γ(·,·)}$-monotone multifunctions. Studia Mathematica, Tome 173 (2006) pp. 197-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-2-6/