Journal of Optimization Theory and Applications

, Volume 134, Issue 3, pp 515–531 | Cite as

Existence of Solutions of Systems of Generalized Implicit Vector Variational Inequalities



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.


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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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  2. 2.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  3. 3.A.G. Anderson Graduate School of ManagementUniversity of CaliforniaRiversideUSA

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