Abstract
In 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.
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Cubiotti, P. An existence theorem for generalized quasi-variational inequalities. Set-Valued Anal 1, 81–87 (1993). https://doi.org/10.1007/BF01039293
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DOI: https://doi.org/10.1007/BF01039293