On The Stability Of The Vector Equilibrium Problem

In this thesis, we study the semicontinuity of a parametric generalized vector quasi-equilibrium problem and the H?lder continuity of solution maps for parametric strong vector equilibrium problems. The detailed contents are listed below:Firstly, in normed vector spaces, we study the parametric generalized vector quasi-equilibrium problem. We study the Hausdorff upper semicontinuity of the solution set map. Then, by introducing a parametric gap function and a constraint qualification, we obtain the Hausdorff lower semicontinuity of the solution set map.Secondly, in metric spaces, we investigate the ( ?C )-lower semicontinuity of set-valued maps and the compactness of solution set for strong vector equilibrium problems. Then, by using these properties, we obtain the H?lder continuity of the solution maps for the parametric strong vector equilibrium problems under the case that the solutions may not be unique.