Existence of Solutions for Generalized Vector Variational-like Inequalities

Abstract

In this paper, we consider a generalized vector variational-like inequality problem (for short, GVVLIP), which includes generalized vector variational inequalities, vector variational inequalities and classical variational inequalities as special cases. The concepts of generalized C-pseudomonotone-like and generalized H-hemicontinuous-like operators are introduced. Some existence results for GVVLIP are obtained under the assumptions of generalized C-pseudomonotone-like property and generalized H-hemicontinuous-like property. These results appear to be new and interesting. New existence results of the classical variational inequality are also obtained.