论文信息 - An existence theorem for generalized quasi-variational inequalities

An existence theorem for generalized quasi-variational inequalities

AbstractIn this paper, we deal with the following generalized quasi-variational inequality problem: given a closed convex subsetX $$ \subseteq$$ ℝn, a multifunction Φ :X → 2ℝn and a multifunction Γ:X → 2X, find a point ( $$(\hat x,\hat z)$$ ) ∈X × ℝn such that $$\hat x in \Gamma (\hat x), \hat z \in \Phi (\hat x)and\left\langle {\hat z,\hat x - y} \right.) \leqslant 0for all y \in \Gamma (\hat x).$$ We prove an existence theorem in which, in particular, the multifunction Φ is not supposed to be upper semicontinuous.

Paolo Cubiotti

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