Mathematical Programming: Series A and B
Finite-dimensional quasi-variational inequalities associated with discontinuous functions
Journal of Optimization Theory and Applications
An application of quasivariational inequalities to linear control systems
Journal of Optimization Theory and Applications
Generalized quasi-variational inequalities in infinite-dimensional normed spaces
Journal of Optimization Theory and Applications
Generalized quasi-variational inequalities without continuities
Journal of Optimization Theory and Applications
Upper Semicontinuity of the Solution set to Parametric Vector Quasivariational Inequalities
Journal of Global Optimization
Discontinuous implicit generalized quasi-variational inequalities in Banach spaces
Journal of Global Optimization
Nash equilibria of generalized games in normed spaces without upper semicontinuity
Journal of Global Optimization
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In this paper, we deal with the following generalized quasi-variational inequality problem: given a real normed space E with topological dual E* and two multifunctions G: X → 2x and F: X→2E*, find (x , φ ) ∈ X × E* such that x∈G(x), φ∈F(x), 〈φ, x-y〉 ≤ 0, for all y ∈ G(x). We extend to such infinite-dimensional setting some existence results which have been obtained recently for the special case where E is finite dimensional. In particular, our assumptions do not imply any kind of continuity for the multifunction F.