Generalized Vector Quasi-Variational Inequality Problems Over Product Sets

Authors:
Q. H. Ansari;S. Schaible;J. C. Yao
Affiliations:
Aff1 Aff2;Mathematical Sciences Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia;Professor, A. G. Anderson Graduate School of Management, University of California, Riverside, U.S.A
Venue:
Journal of Global Optimization
Year:
2005

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Abstract

In this paper we consider vector quasi-variational inequality problems over product sets (in short, VQVIP). Moreover we study generalizations of this model, namely problems of a system of vector quasi-variational inequalities (in short, SVQVIP), generalized vector quasi-variational inequality problems over product sets (in short, GVQVIP) and problems of a system of generalized vector quasi-variational inequalities (in short, SGVQVIP). We show that every solution of (VQVIP) (respectively, (GVQVIP)) is a solution of (SVQVIP) (respectively, (SGVQVIP)). By defining relatively pseudomonotone and relatively maximal pseudomonotone maps and by employing a known fixed point theorem, we establish the existence of a solution of (VQVIP) and (SVQVIP). These existence results are then used to derive the existence of a solution of (GVQVIP) and (SGVQVIP), respectively, The results of this paper extend recent results in the literature. They are obtained in a more general setting.