@article {
author = {Sadeqi, Ildar and Hassankhali, Sima},
title = {On Polar Cones and Differentiability in Reflexive Banach Spaces},
journal = {Sahand Communications in Mathematical Analysis},
volume = {11},
number = {1},
pages = {13-23},
year = {2018},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2018.72221.284},
abstract = {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 ${\mathop{\rm int}}(\mathrm{dom} \sigma_C)$.},
keywords = {Recession cone,Polar cone,Bounded base,Support function,Gateaux differentiability},
url = {https://scma.maragheh.ac.ir/article_32215.html},
eprint = {https://scma.maragheh.ac.ir/article_32215_2e744dde303f4e6c175af724da107e48.pdf}
}