Existence of solutions of vector variational inequalities and vector complementarity problems

Authors:
Q. H. Ansari;A. P. Farajzadeh;S. Schaible
Affiliations:
Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia 31261 and Department of Mathematics, Aligarh Muslim University, Aligarh, India 202 002;Department of Mathematics, Razi University, Kermanshah, Iran 67149;Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taiwan 32023
Venue:
Journal of Global Optimization
Year:
2009

Citing 2
Cited 2

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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.