On the Solution Existence of Generalized Quasivariational Inequalities with Discontinuous Multifunctions |
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Authors: | B T Kien N C Wong J C Yao |
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Institution: | (1) Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC |
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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
and a multifunction Γ:X→2
X
, find a point
such that
,
. 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.
The authors express their sincere gratitude to the referees for helpful suggestions and comments.
This research was partially supported by a grant from the National Science Council of Taiwan, ROC.
B.T. Kien was on leave from National University of Civil Engineering, Hanoi, Vietnam. |
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Keywords: | Generalized quasivariational inequalities Lower semicontinuity Hausdorff upper semicontinuity Hausdorff lower semicontinuity Multifunctions Closed graphs Open graphs |
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