Geodesic
On ${\mit\Phi}^{\gamma(\cdot,\cdot)}$-subdifferentiable and $[{\mit\Phi}+\gamma]$-subdifferentiable Functions
S. Rolewicz1
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 3, pp. 273-279.

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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.
DOI : 10.4064/ba53-3-4
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

S. Rolewicz 1

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland 
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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. http://geodesic.mathdoc.fr/articles/10.4064/ba53-3-4/

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