Journal of Optimization Theory and Applications

, Volume 83, Issue 2, pp 391–403

Multi-valued variational inequalities with K-pseudomonotone operators

  • J. C. Yao
Contributed Papers

DOI: 10.1007/BF02190064

Cite this article as:
Yao, J.C. J Optim Theory Appl (1994) 83: 391. doi:10.1007/BF02190064


In this paper, we first employ the 1961 celebrated Fan lemma to derive a very general existence result for multi-valued variational inequalities involving multi-valued K-pseudomonotone operators. It will be seen that this result improves and unifies existence results of variational inequalities for monotone operators. Next, we establish some uniqueness results for multi-valued variational inequalities by introducing the concepts of strict, α, and strong K-pseudomonotonicity of multi-valued operators, respectively. These uniqueness results appear to be new even if the underlying space is finite-dimensional.

Key Words

Multi-valued variational inequalitiesK-pseudomonotone operatorsstrictly K-pseudomonotone operatorsstrongly K-pseudomonotone operatorsupper semicontinuous operators

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • J. C. Yao
    • 1
  1. 1.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungTaiwan, ROC