无穷维自反空间中集值映射的弱导数及其应用

The Weak Derivatives of Set-valued Map in Infinite Dimensional Reflexive Space and Its Applications

用无穷维空间的弱拓扑引入弱相依锥T k(x)和弱P锥P k(x)及与它们相应的弱导数D F(x ,y)和P F(x ,y) ;研究弱导数的链式法则和弱Lip连续性 ;作为应用 。

The?definition?of?two?weak?tangent?cones?are?given?by?using?the?weak?topology,?and?accordingly,the?concerpt?of?the?weak?derivatives?and?their?chain?rules?and?weak lip?continuity?are?studied.Finally,as?an?application,we?proved?a?theorem?concerning?whether?the?set valued?map?F:X→Y?is?locally?injective?or?inversely?injective.