Generalized bi-quasi-variational inequalities (Q1263807)

The author deals with the generalized bi-quasivariational inequality problem: find \(\hat y\in X\) such that \(\hat y\in S(\hat y)\) and \(\inf_{w\in T(\hat y)}Re<f-w,\hat y-x>\leq 0\) for all \(x\in S(\hat y)\) and \(f\in M(\hat y)\), where \(X\subset E\), S: \(X\to 2^ X\) is a multivalued map, M,T: \(X\to 2^ F\) and E, F are Hausdorff topological vector spaces. Two existence theorems are verified.