光滑Banach空间上扩张值函数的Frechet次微分

Frechet Subdifferentials of Extended Functions in Smooth Banach Spaces

中文关键词:  次微分  光滑空间  解藕下确界  法向锥  多方向中值不等式

英文关键词:Frechet subdifferential  smooth Banach spaces  decoupled infimum  normal cone  multidirectional mean value inequality.

中文摘要:

      首先证明了Frechet光滑Banach空间上齐次函数的次微分的一个有用定理,然后利用下半连续函数和的次微分规则把Clarke-Ledyaev多方向中值不等式推广到多个函数的情形.

英文摘要:

      We obtain a useful result about Frechet subdifferentials of homogeneous function defined in Frechet smooth Banach space. Then we extend the Clarke-Ledyaev multidh-ectional mean value inequality to a group of functions by use of the sum rules for Frechet subdifferentials of lower semicontinuous functions.