Generalized Vector Quasivariational Inclusion Problems with Moving Cones

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), where A:E×K→2^K, B:E×K→2 ^E , C:E×K→2 ^Y , F,G:E×K×K→2 ^Y 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).