TY - JOUR
ID - 32215
TI - On Polar Cones and Differentiability in Reflexive Banach Spaces
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Sadeqi, Ildar
AU - Hassankhali, Sima
AD - Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
AD - Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
Y1 - 2018
PY - 2018
VL - 11
IS - 1
SP - 13
EP - 23
KW - Recession cone
KW - Polar cone
KW - Bounded base
KW - Support function
KW - Gateaux differentiability
DO - 10.22130/scma.2018.72221.284
N2 - Let $X$ be a Banach space, $C\subset X$ be a closed convex set included in a well-based cone $K$, and also let $\sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set $C$, so that ${\mathop{\rm int}}(\mathrm{dom} \sigma_C) \neq\emptyset$. The latter is a primary condition for subdifferentiability of the support function $\sigma_C$. Eventually, we study Gateaux differentiability of support function $\sigma_C$ on two sets, the polar cone of $K$ and ${\mathop{\rm int}}(\mathrm{dom} \sigma_C)$.
UR - https://scma.maragheh.ac.ir/article_32215.html
L1 - https://scma.maragheh.ac.ir/article_32215_2e744dde303f4e6c175af724da107e48.pdf
ER -