Banach空间包含方程随机解的存在性

Existence of Random Solutions to the Inclusion Equations in Banach Space

在Banach空间中讨论了集值系统x(w)∈F(w ,x(w) ,y(w) ) ,y(w) ∈G(w ,x(w) ,y(w) ) 随机解的存在性。

Let E be a compact convex subset of a Banach space.(Ω,A) a measurable space. Let F and G:Ω×E×E→CK(E) be mappings such that for each f∈C(E),w∈Ω,x∈E,F(w,x,f(x)) and G(w,x,f(x)) are continuous random operators and F(w,x,·) is k(w)Lipschitz and moreover H(G(w,x,y 1),G(w,x,y 2))≤q(w){d(y 1,G(w,x,y 1))+d(y 2,G(w,x,y 2))} for any w∈Ω, x,y 1,y 2∈E,q(w):Ω→(0,12). Then there measurable mappings u and v:Ω→E such that u(w)∈F(w,u(w),v(w)) and v(w)∈G(w,u(w),v(w)).