Applications of pseudo-monotone operators with some kind of upper semicontinuity in generalized quasi-variational inequalities on non-compact sets
Mohammad S. R. Chowdhury, Kok-Keong Tan · Proceedings of the American Mathematical Society · 1998
Let E E be a topological vector space and X X be a non-empty subset of E E . Let S : X → 2 X S:X\rightarrow 2^{X} and T : X → 2 E ∗ T:X\rightarrow 2^{E^{*}} be two maps. Then the generalized quasi-variational inequality (GQVI) problem is to find a point y ^ ∈ S ( y ^ ) \hat y\in S(\hat y) and a point w ^ ∈ T ( y ^ ) \hat w\in T(\hat y) such that R e ⟨ w ^ , y ^ − x ⟩ ≤ 0 Re\