On the Rockafellar theorem for ${\Phi }^{\gamma (·,·)}$-monotone multifunctions

S. Rolewicz. "On the Rockafellar theorem for $Φ^{γ(·,·)}$-monotone multifunctions." Studia Mathematica 172.2 (2006): 197-202. <http://eudml.org/doc/284965>.

@article{S2006,
abstract = {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 $Γ: X → 2^\{Φ\}$ be a cyclic $Φ^\{γ(·,·)\}$-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 $Φ^\{γ(·,·)\}$-subdifferential of f, $Γ(x) ⊂ ∂_\{Φ\}^\{γ(·,·)\} f|_\{x\}$.},
author = {S. Rolewicz},
journal = {Studia Mathematica},
keywords = {; ); cyclic ; )},
language = {eng},
number = {2},
pages = {197-202},
title = {On the Rockafellar theorem for $Φ^\{γ(·,·)\}$-monotone multifunctions},
url = {http://eudml.org/doc/284965},
volume = {172},
year = {2006},
}

TY - JOUR
AU - S. Rolewicz
TI - On the Rockafellar theorem for $Φ^{γ(·,·)}$-monotone multifunctions
JO - Studia Mathematica
PY - 2006
VL - 172
IS - 2
SP - 197
EP - 202
AB - 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 $Γ: X → 2^{Φ}$ be a cyclic $Φ^{γ(·,·)}$-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 $Φ^{γ(·,·)}$-subdifferential of f, $Γ(x) ⊂ ∂_{Φ}^{γ(·,·)} f|_{x}$.
LA - eng
KW - ; ); cyclic ; )
UR - http://eudml.org/doc/284965
ER -