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Nonlinear mixed vector variational inequality problems. (English) Zbl 1259.49015

Summary: In this paper, we consider nonlinear mixed vector variational inequality problems in the setting of topological vector spaces. We extend the concept of upper sign continuity for vector-valued functions and establish some existence results for solutions of vector variational inequalities. By utilizing a new version of the Ky Fan lemma we investigate the non-emptyness and compactness of the solution sets of these problems under some suitable assumptions.

MSC:

49J40 Variational inequalities
47H10 Fixed-point theorems
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces