 Generalized Quasi-Variational Inequalities Without ContinuitiesP. Cubiotti Journal of Optimization Theory and Applications, 1997, vol. 92, issue 3, No 3, 477-495 Abstract: Abstract Given a nonempty set $$X \subseteq \mathbb{R}^n $$ and two multifunctions $$\beta :X \to 2^X ,\phi :X \to 2^{\mathbb{R}^n } $$ , we consider the following generalized quasi-variational inequality problem associated with X, β φ: Find $$(\bar x,\bar z) \in X \times \mathbb{R}^n $$ such that $$\bar x \in \beta (\bar x),\bar z \in \phi (\bar x){\text{, and sup}}_{y \in \beta (\bar x)} \left\langle {\bar z,\bar x - y} \right\rangle \leqslant 0$$ . We prove several existence results in which the multifunction φ is not supposed to have any continuity property. Among others, we extend the results obtained in Ref. 1 for the case β(x(≡X. Keywords: Generalized quasi-variational inequalities; upper semicontinuous multifunctions; lower semicontinuous multifunctions; fixed points (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:92:y:1997:i:3:d:10.1023_a:1022699205336 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull More articles in Journal of Optimization Theory and Applications from Springer |
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