Existence of Solutions of Systems of Generalized Implicit Vector Variational Inequalities |
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Authors: | S Al-Homidan Q H Ansari S Schaible |
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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;(3) A.G. Anderson Graduate School of Management, University of California, Riverside, CA, USA |
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Abstract: | We consider five different types of systems of generalized vector variational inequalities and derive relationships among
them. We introduce the concept of pseudomonotonicity for a family of multivalued maps and prove the existence of weak solutions
of these problems under these pseudomonotonicity assumptions in the setting of Hausdorff topological vector spaces as well
as real Banach spaces. We also establish the existence of a strong solution of our problems under lower semicontinuity for
a family of multivalued maps involved in the formulation of the problems. By using a nonlinear scalar function, we introduce
gap functions for our problems by which we can solve systems of generalized vector variational inequalities using optimization
techniques.
The first two authors were supported by SABIC and Fast Track Research Grants SAB-2006-05. They are grateful to the Department
of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing excellent research
facilities. |
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Keywords: | Systems of generalized implicit vector variational inequalities Pseudomonotonicity Existence results for a solution Gap functions Lower semicontinuity Upper hemicontinuity ℋ -Hemicontinuity |
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