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 |