| 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] |
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| 一类集值映射的高阶微分 |
| 吴孟达 |
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(系统工程与应用数学系)
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| 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: |
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| On Higher Order Differentials of One Class Multifunctions |
| Wu Mengda |
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(Department of Applied Mathematics and System Engineering)
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| 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 |
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