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On discontinuous quasi-variational inequalities

Liang-Ju Chu; Ching-Yang Lin — 2007

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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 $T : X \to 2^{X *}$ and $S : C \to 2^{D}$ 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...

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