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

作　　者：柴正猛[1] 

机构地区：[1]云南民族学院数学与计算机科学系,云南昆明650031

出　　处：《Journal of Mathematical Research and Exposition》2003年第1期121-128,共8页数学研究与评论（英文版）

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)判定无穷维自反空间X到Banach空间Y的集值映射F是否具有单值性和逆单值性的一个判定定理及其推论.In this paper,we first studied the existence of the equilbrum of the set-valued mapF: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 Tσk(x),the chainrule of the weak contingent derivative DσF(x,y),and the weak lipschitz continuity of the y-weak derivative Dσy(x,y).Finally,as an application,by using Dσ(x,y)and the weakparatingent derivative Pσy(x,y),we proved a theorem and its corollary concerning whetherF:X→Y from reflexive space X to Banaeh space Y is locally injective and whether it is in-versely injective.

关 键 词：赋范线性空间 包含方程 可解性定理 弱切锥 序列弱聚点 弱拓扑 

分 类 号：O177.3[理学—数学]