# On discontinuous quasi-variational inequalities

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

- Volume: 27, Issue: 2, page 199-212
- ISSN: 1509-9407

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topLiang-Ju Chu, and Ching-Yang Lin. "On discontinuous quasi-variational inequalities." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.2 (2007): 199-212. <http://eudml.org/doc/271142>.

@article{Liang2007,

abstract = {In this paper, we derive a general theorem concerning the quasi-variational inequality problem: find x̅ ∈ C and y̅ ∈ T(x̅) such that x̅ ∈ S(x̅) and
⟨y̅,z-x̅⟩ ≥ 0, ∀ z ∈ S(x̅),
where C,D are two closed convex subsets of a normed linear space X with dual X*, and $T:X → 2^\{X*\}$ and $S:C → 2^D$ are multifunctions. In fact, we extend the above to an existence result proposed by Ricceri [12] for the case where the multifunction T is required only to satisfy some general assumption without any continuity. Under a kind of Karmardian’s condition, we give a partial affirmative answer to an unbounded quasi-variational inequality problem.},

author = {Liang-Ju Chu, Ching-Yang Lin},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {variational inequality; quasi-variatioal inequality; Ricceri's conjecture; Karamardian condition; Hausdorff continuous multifunction; Kneser's minimax inequality},

language = {eng},

number = {2},

pages = {199-212},

title = {On discontinuous quasi-variational inequalities},

url = {http://eudml.org/doc/271142},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Liang-Ju Chu

AU - Ching-Yang Lin

TI - On discontinuous quasi-variational inequalities

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2007

VL - 27

IS - 2

SP - 199

EP - 212

AB - In this paper, we derive a general theorem concerning the quasi-variational inequality problem: find x̅ ∈ C and y̅ ∈ T(x̅) such that x̅ ∈ S(x̅) and
⟨y̅,z-x̅⟩ ≥ 0, ∀ z ∈ S(x̅),
where C,D are two closed convex subsets of a normed linear space X with dual X*, and $T:X → 2^{X*}$ and $S:C → 2^D$ are multifunctions. In fact, we extend the above to an existence result proposed by Ricceri [12] for the case where the multifunction T is required only to satisfy some general assumption without any continuity. Under a kind of Karmardian’s condition, we give a partial affirmative answer to an unbounded quasi-variational inequality problem.

LA - eng

KW - variational inequality; quasi-variatioal inequality; Ricceri's conjecture; Karamardian condition; Hausdorff continuous multifunction; Kneser's minimax inequality

UR - http://eudml.org/doc/271142

ER -

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- [12] B. Ricceri, Basic existence theorem for generalized variational and quasi-variational inequalities, Variational Inequalities and Network Equilibrium Problems, Edited by F. Giannessi and A. Maugeri, Plenum Press, New York, 1995 (251-255). Zbl0847.49011
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