Journal of Global Optimization

, Volume 36, Issue 4, pp 483–497

Existence of Solutions of Generalized Vector Variational Inequalities in Reflexive Banach Spaces


DOI: 10.1007/s10898-005-5509-6

Cite this article as:
Zeng, LC. & Yao, JC. J Glob Optim (2006) 36: 483. doi:10.1007/s10898-005-5509-6


The purpose of this paper is to study the solvability for a class of generalized vector variational inequalities in reflexive Banach spaces. Utilizing the KKM-Fan lemma and the Nadler’s result, we prove the solvability results for this class of generalized vector variational inequalities for monotone vector multifuctions. On the other hand, we first introduce the concepts of complete semicontinuity and strong semicontinuity for vector multifunctions. Then we prove the solvability for this class of generalized vector variational inequalities without monotonicity assumption by using these concepts and by applying the Brouwer fixed point theorem. The results in this paper are extension and improvement of the corresponding results in Huang and Fang (2006).


Brouwer fixed point theoremComplete semicontinuityGeneralized vector variational inequalitiesHausdorff metricKKM-Fan lemma

Mathematics Subject Classification (2000)


Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina
  2. 2.Department of Applied MathematicsNational Sun Yat-sen UniversityKaohsiungTaiwan, R.O.C