Existence And Stability Of Solutions For Generalized Vector Variational- Like Inequalities

Variatioal inequality has widely applications in many fields, such as economy, engineering and transportation. Existence of solutions for variational inequalities problems is studied all the time, the theory of stability and sensitivity analysis for variatioal inequalities is a hotspot in the research of mathematics. This thesis mainly studies the existence and stability of solutions for a new class of generalized vector variational-like inequality in Hausdorff topological vector spaces and sensitivity analysis for a class of generalized parametric implicit mixed quasi-variational inequalities in Hilbert spaces.In this thesis, the main research results can be summarized as follows:The second chapter introduces a class of generalized vector variational-like inequalities in Hausdorff topological vector spaces, under the suitable conditions, we study the existence of solutions for the generalized vector variational-like inequality by using the Fan-KKM theorem, furthermore, we study upper semicontinuity and lower semicontinuity of solution mappings for the generalized vector variational-like inequality, thus we get stability results of the solution mappings.The third chapter introduces a class of generalized parametric mixed quasi-variational inequalities in Hilbert spaces, by using the projection method and set-valued contractive mapping fixed point theorem, existence of the solution for the generalized parametric mixed quasi-variational inequality is proved with the suitable conditions and we study sensitivity of solution mapping.