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On discontinuous quasi-variational inequalities

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Chu L.-J., Lin C.-Y.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2007

tom 27

nr 2

199-212

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.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Chu L.-J.

1 Lin C.-Y.

1 2007

Wyniki wyszukiwania

On discontinuous quasi-variational inequalities