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

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.

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T_k^σ(x)的直接像,弱相依导数D^σF(x,y)的一个链式法则以及偏y弱导数D_y^σF(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D^σF(x,y)及弱P导数P^σF(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 T_k^σ(x),the chainrule of the weak contingent derivative D^σF(x,y),and the weak lipschitz continuity of the y-weak derivative D_y^σ(x,y).Finally,as an application,by using D^σ(x,y)and the weak paratingent derivative P^σF(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.