Weighted Variational Inequalities |
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Authors: | Q H Ansari Z Khan A H Siddiqi |
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Institution: | (1) Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia;(2) Department of Mathematics, Aligarh Muslim University, Aligarh, India |
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Abstract: | In this paper, we introduce weighted variational inequalities over product of sets and system of weighted variational inequalities.
It is noted that the weighted variational inequality problem over product of sets and the problem of system of weighted variational
inequalities are equivalent. We give a relationship between system of weighted variational inequalities and systems of vector
variational inequalities. We define several kinds of weighted monotonicities and establish several existence results for the
solution of the above-mentioned problems under these weighted monotonicities. We introduce also the weighted generalized variational
inequalities over product of sets, that is, weighted variational inequalities for multivalued maps and systems of weighted
generalized variational inequalities. Extensions of weighted monotonicities for multivalued maps are also considered. The
existence of a solution of weighted generalized variational inequalities over product of sets is also studied. The existence
results for a solution of weighted generalized variational inequality problem give also the existence of solutions of systems
of generalized vector variational inequalities.
The first and third author express their thanks to the Department of Mathematical Sciences, King Fahd University of Petroleum
and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities. The authors are also grateful to the referees
for comments and suggestions improving the final draft of this paper. |
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Keywords: | Weighted variational inequalities system of vector variational inequalities weighted generalized variational inequalities system of generalized vector variational inequalities Nash equilibrium problems |
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