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2007 | 27 | 2 | 199-212
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On discontinuous quasi-variational inequalities

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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.
  • Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, Republic of China
  • Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, Republic of China
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