On Existences Of Solutions For Generalized Variational Inequality Problems

In this thesis, we study two problems: Existences of solutions for generalized quasi- variational inequalities with pseudomonotone operators in the sense of Brézis and existences of solutions for generalized vector variational inequalities with a set-valued H-Semi- Pseudomonotone mapping. The detailed contents are listed below:Firstly, by the existences of solutions for the variational inequalities in the finite dimensional space, we proved the existences of solutions for generalized variational inequalities and generalized quasi-variatonal inequalities with pseudo-monotone operator in the sense of Brézis. We also established two existence theorems for generalized variational inequalities in topological vector spaces and generalized quasi-variational inequalities in Hausdorff locally convex space, respectively.Secondly, we generalize the concept of set-valued semi-monotonicity to a set-valued H-semi-pseudomonotone mapping and then consider a generalized vector variational inequality problem concerning the vector set-valued H-Semi-Pseudomonotone mapping by using the Kakutani–Fan–Glicksberg fixed point theorem, Several existence results are obtained in reflexive Banach space.