Sensitivity Analysis For Related Mixed Vector Equilibrium Problems

There are closely related between equilibrium problem and these including game theory, physics and mechanics, economy and finance, control and optimization problems, fixed point of operator and variational inequality theory. Because it has important application in many fields, so much attention is paid by the scholars.In recent years, it becomes a very popular branch field of nonlinear analysis and obtains a lot of meaningful results. The researches of this field mainly involve three aspects, namely the existence of solutions to equilibrium problems, constructing some iterative algorithms of solution to solve such problems and proving the convergence of algorithms, the sensitivity analysis of the solutions.In recent years, due to the need of the mathematical theory and practical application, many researchers have extended the study to vector equilibrium problems. They expanded study on the existence and stability of solutions for various types of vector equilibrium problems. This thesis mainly studies sensitivity analysis of solutions for parametric mixed implicit vector equilibrium problem and Holder continuity of solution sets for parametric generalized mixed vector quasi-equilibrium problems. In the thesis, we will study these problems including following three parts.Firstly, using the KKM theory, we establish sufficient conditions to ensure the existence of solutions for parametric mixed implicit vector equilibrium problem, and then we study upper semi-continuity and lower semi-continuity of solutions for such problem. Thus we summarize the continuity of the solution mapping. These results extend the work of Nanjing Huang, Jun Li et al.Secondly, we establish the more generalized conditions for the Holder continuity of solution mappings to parametric generalized mixed vector quasi-equilibrium problems under the case that solution mappings are set-valued in metric spaces. Furthermore, basing on the study of Holder continuity, we further derive upper bounds for the distance between a solution set of parametric generalized mixed vector quasi-equilibrium problems with fixed parameters and an approximate solution. These results extend the work of L. Q. Anh, P. Q. Khanh, S. J. Li et al.Finally, using cone interval, we quote a new description of Holder continuity, putting forward by S. J. Li, Z. Y. Peng et al, to study the conditions of another Holder continuity of the solution mapping for parametric generalized mixed vector quasi-equilibrium problem in the linear metric space with cone. These conclusions extend the study of S. J. Li, Z. Y. Peng, et al.