Existence theorems for generalized vector variational inequalities with a variable ordering relation

@article{Ceng2010ExistenceTF,
  title={Existence theorems for generalized vector variational inequalities with a variable ordering relation},
  author={Lu-Chuan Ceng and Shuechin Huang},
  journal={J. Global Optimization},
  year={2010},
  volume={46},
  pages={521-535}
}
In this paper we study the solvability of the generalized vector variational inequality problem, the GVVI problem, with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVVIs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVVI problems without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are… CONTINUE READING