Abstract
In this paper, we introduce a generalized vector variational inequality problem (GVVIP) which extends and unifies vector variational inequalities as well as classical variational inequalities in the literature. The concepts of generalized C-pseudomonotone and generalized hemicontinuous operators are introduced. Some existence results for GVVIP are obtained with the assumptions of generalized C-pseudomonotonicity and generalized hemicontinuity. These results appear to be new and interesting. New existence results of the classical variational inequality are also obtained.
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Lin, K.L., Yang, D.P. & Yao, J.C. Generalized Vector Variational Inequalities. Journal of Optimization Theory and Applications 92, 117–125 (1997). https://doi.org/10.1023/A:1022640130410
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DOI: https://doi.org/10.1023/A:1022640130410