Generalized quasivariational inequalities in locally convex topological vector spaces (Q1110083)

Let E be a Hausdorff topological vector space and X an arbitrary nonempty subset of E. Given a point-to-set map S: \(X\to 2^ X\) and a point-to-set map T: \(X\to 2^{E'}\) (where E' is the dual space of E with the pairing (w,x) for \(w\in E'\) and \(x\in X)\), the generalized quasivariational inequality problem (GQVI) is to find a point \(y^*\in S(y^*)\) and a point \(u^*\in T(y^*)\) such that \(Re(u^*,y^*-x)\leq 0\) for all \(x\in S(y^*)\). Several results on the existence of a solution to the above GQVI are established by using the Ky Fan minimax principle.