Abstract
In this paper, we consider vector variational inequality and vector F-complementarity problems in the setting of topological vector spaces. We extend the concept of upper sign continuity for vector-valued functions and provide some existence results for solutions of vector variational inequalities and vector F-complementarity problems. Moreover, the nonemptyness and compactness of solution sets of these problems are investigated under suitable assumptions. We use a version of Fan-KKM theorem and Dobrowolski’s fixed point theorem to establish our results. The results of this paper generalize and improve several results recently appeared in the literature.
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Ansari, Q.H., Farajzadeh, A.P. & Schaible, S. Existence of solutions of vector variational inequalities and vector complementarity problems. J Glob Optim 45, 297–307 (2009). https://doi.org/10.1007/s10898-008-9375-x
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DOI: https://doi.org/10.1007/s10898-008-9375-x