Star-shaped Differentiable Functions and Star-shaped Differentials

被引：0
|
作者：
Pan Shao-rong 1
机构：
来源：
Communications in Mathematical Research | 2010年 / 26卷 / 01期
关键词：
The space of star-shaped sets; gauge function; isometrical isomorphism; directionally differentiable function; star-shaped differential; mean-value theorem;
D O I：
10.13447/j.1674-5647.2010.01.002
中图分类号：
O172.2 [积分学]; O174.13 [凸函数、凸集理论];
学科分类号：
0701 ; 070101 ; 070104 ;
摘要：
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.
引用
收藏
页码：41 / 52
页数：12
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