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Quasimonotone variational inequalities in Banach spaces. (English) Zbl 0904.49005

Existence results for variational inequality problems are derived under the quasimonotone condition in Banach spaces. This condition seems much weaker than the pseudomonotone condition which was employed earlier to show the existence of the problem. Another condition that is used in the paper is that the ground set has a nonempty inner point. This condition is weaker than the condition that the ground set is closed convex in separable Banach spaces.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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