Generalized Vector Quasivariational Inclusion Problems with Moving Cones

[[abstract]]This paper deals with the generalized vector quasivariational inclusion Problem (P1) (resp. Problem (P2)) of finding a point (z0, x0) of a set E × K such that (z0, x0) ∈ B(z0, x0)×A(z0, x0) and, for all η ∈ A(z0, x0), F(z0, x0,η) ⊂ G(z0, x0, x0)+C(z0, x0) [resp.F (z0, x0, x0) ⊂ G(z0, x0,η)+ C(z0, x0)], where A : E×K →2K, B : E×K →2E, C : E×K →2Y , F,G: E×K×K →2Y are some set-valued maps and Y is a topological vector space. The nonemptiness and compactness of the solution sets of Problems (P1) and (P2) are established under the verifiable assumption that the graph of the moving cone C is closed and that the setvalued maps F and G are C-semicontinuous in a new sense (weaker than the usual sense of semicontinuity)