On ${\mit\Phi}^{\gamma(\cdot,\cdot)}$-subdifferentiable
and $[{\mit\Phi}+\gamma]$-subdifferentiable Functions
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 3, pp. 273-279
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $X$ be an arbitrary set. Let ${\mit\Phi}$ be a family of
real-valued functions defined on $X$.
Let $\gamma:X\times
X\to \mathbb R$. Set
$[{\mit\Phi}+\gamma]=\{ \phi(\cdot)+ \gamma(\cdot,x)\mid \phi \in {\mit\Phi},\, x \in X\}$.
We give conditions guaranteeing the equivalence of
${\mit\Phi}^{\gamma(\cdot,\cdot)}$-subdifferentiability
and $[{\mit\Phi}+\gamma]$-subdifferentiability.
Keywords:
arbitrary set mit phi family real valued functions defined gamma times mathbb set mit phi gamma phi cdot gamma cdot mid phi mit phi conditions guaranteeing equivalence mit phi gamma cdot cdot subdifferentiability mit phi gamma subdifferentiability
Affiliations des auteurs :
S. Rolewicz 1
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title = {On ${\mit\Phi}^{\gamma(\cdot,\cdot)}$-subdifferentiable
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journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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S. Rolewicz. On ${\mit\Phi}^{\gamma(\cdot,\cdot)}$-subdifferentiable
and $[{\mit\Phi}+\gamma]$-subdifferentiable Functions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 3, pp. 273-279. doi: 10.4064/ba53-3-4
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