The Extensions of the Solvable Theorem of Inclusion Equation and the Applications of the Weak Tangent Cones in Normed Linear Space
Chai Zheng-meng · Journal of Mathematical Research and Exposition · 2003
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.