| 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 Tkσ(x),the chainrule of the weak contingent derivative DσF(x,y),and the weak lipschitz continuity of the y-weak derivative Dyσ(x,y).Finally,as an application,by using Dσ(x,y)and the weak paratingent derivative PσF(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. |
