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.
