Abstract

This paper deals with the generalized vector quasivariational inclusion Problem (P1) (resp. Problem (P2)) of finding a point (z 0,x 0) of a set E×K such that (z 0,x 0)∈B(z 0,x 0)×A(z 0,x 0) and, for all η∈A(z 0,x 0), 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 set-valued maps F and G are C-semicontinuous in a new sense (weaker than the usual sense of semicontinuity).