引用本文: | 吴孟达.一类集值映射的高阶微分[J].国防科技大学学报,1990,12(1):35-41.[点击复制] |
Wu Mengda.On Higher Order Differentials of One Class Multifunctions[J].Journal of National University of Defense Technology,1990,12(1):35-41[点击复制] |
|
|
|
本文已被:浏览 5147次 下载 5056次 |
一类集值映射的高阶微分 |
吴孟达 |
(系统工程与应用数学系)
|
摘要: |
在文[I]中,H.T.Banks与M.Q.Jacobs讨论了集映?:Rm→A(Rn)的一阶微分,分别给出了?可微的充分条件与必要条件。本文改进了文[l]的工作,证明了[1]中条件(3.2) 的限制是不必要的,从而得到了?可微的充分必要条件,及较为简洁的?微分解析表达式。在文中也讨论了?的K阶微分,得到了?k阶可微的充分必要条件及k阶微分的解析表达式。 |
关键词: 集值映射,Hausdorff 距离,集映微分,集映高阶微分 |
DOI: |
投稿日期:1988-06-06 |
基金项目: |
|
On Higher Order Differentials of One Class Multifunctions |
Wu Mengda |
(Department of Applied Mathematics and System Engineering)
|
Abstract: |
In the paper [l], H.T.Banks and M.Q.Jacobs have discussed the one order differential of the multifuntions ?:Rm→A(Rn),Their result has been improved in this paper and the sufficient and necessary conditions for the differentiability are given respectively. The limitation of (3.2) in [l] is proved to be unnecessary and the sufficient and necessary conditions for the differentialbility of ? are found. Furthermore,the sufficient and necessary conditions for the higher order differentialbility of ? are gained and a calculus formula is given. |
Keywords: multifunction,Hausdorff metric,differential of the multifunction,higher order differential of multifunction |
|
|