| 柴正猛.赋范线性空间中包含方程可解性定理的推广及弱切锥的应用[J].数学研究及应用,2003,23(1):121~128 |
| 赋范线性空间中包含方程可解性定理的推广及弱切锥的应用 |
| The Extensions of the Solvable Theorem of Inclusion Equation and the Applications of the Weak Tangent Cones in Normed Linear Space |
| 投稿时间：1999-10-03 |
| DOI：10.3770/j.issn:1000-341X.2003.01.019 |
| 中文关键词: 序列弱聚点 弱拓扑 切锥 |
| 英文关键词:weak sequence cluster weak topology tangent cone. |
| 基金项目: |
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| 中文摘要: |
| 本文首先在一般的赋范线性空间中研究了集值映射F;X→Y的平衡点的存在性问题,证明了包含问题O∈F(X)的三个可解性定理.然后在无穷维空间中研究了弱相依锥Tkσ(x)的直接像,弱相依导数DσF(x,y)的一个链式法则以及偏y弱导数DyσF(x,y)的弱Lip连续性.最后,作为应用,给出并证明了用弱相依导数DσF(x,y)及弱P导数PσF(x,y)判定无穷维 |
| 英文摘要: |
| In this paper,we first studied the existence of the equilbrum of the set-valued map F:X→Y from Banach space X to Banach space Y,and got three solvable theorems of the in-clusion 0 ∈F(x),which extended the theorem of [1].Then,in infinite dimensional linearnormed space,we studied the direct image of the weak contingent cone Tkσ(x),the chainrule of the weak contingent derivative DσF(x,y),and the weak lipschitz continuity of the y-weak derivative Dyσ(x,y).Finally,as an application,by using Dσ(x,y)and the weak paratingent derivative PσF(x,y), we proved a theorem and its corollary concerning whether F:X→Y from reflexive space X to Banach space Y is locally injective and whether it is inversely injective. |
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