On the Solution Existence of Generalized Quasivariational Inequalities with Discontinuous Multifunctions

B. T. Kien, N. C. Wong and J. C. Yao ()
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B. T. Kien: National Sun Yat-Sen University
N. C. Wong: National Sun Yat-Sen University
J. C. Yao: National Sun Yat-Sen University

Journal of Optimization Theory and Applications, 2007, vol. 135, issue 3, No 14, 515-530

Abstract: Abstract We study the following generalized quasivariational inequality problem: given a closed convex set X in a normed space E with the dual E *, a multifunction $\Phi :X\rightarrow 2^{E^{*}}$ and a multifunction Γ:X→2 X , find a point $(\hat{x},\hat{z})\in X\times E^{*}$ such that $\hat{x}\in \Gamma(\hat{x}),\hat{z}\in \Phi (\hat{x}),\langle \hat{z},\hat{x}-y\rangle \leq 0$ , $\forall y\in \Gamma(\hat{x})$ . We prove some existence theorems in which Φ may be discontinuous, X may be unbounded, and Γ is not assumed to be Hausdorff lower semicontinuous.

Keywords: Generalized quasivariational inequalities; Lower semicontinuity; Hausdorff upper semicontinuity; Hausdorff lower semicontinuity; Multifunctions; Closed graphs; Open graphs (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-007-9239-4

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