TY - JOUR
T1 - Star-Shaped Differentiable Functions and Star-Shaped Differentials
AU - Pan , Shaorong
AU - Zhang , Hongwei
AU - Zhang , Liwei
JO - Communications in Mathematical Research 
VL - 1
SP - 41
EP - 52
PY - 2021
DA - 2021/05
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19176.html
KW - The space of star-shaped sets, gauge function, isometrical isomorphism,
directionally differentiable function, star-shaped differential, mean-value theorem.
AB - <p style="text-align: justify;">Based on the isomorphism between the space of star-shaped sets and the
space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped
differential of a pointwise maximum and a pointwise minimum of a finite number of
directionally differentiable functions, and a composite of two directionally differentiable functions are derived. Furthermore, the mean-value theorem for a directionally
differentiable function is demonstrated.</p>