含参原始向量混合拟均衡问题和含参对偶向量混合拟均衡问题解的H\"{o}lder 连续性

H\"{o}lder continuity of solutions to parametric primal and dual vector mixed quasi-equilibrium problems

摘要:

本文将对偶法则应用于均衡问题，提出了含参对偶向量混合拟均衡问题即混合Minty-type含参对偶向量混合拟均衡问题，其次在更一般的集合上研究含参原始向量混合拟均衡问题(PVMQEPi)(i=1,2)和含参对偶向量混合拟均衡问题(DVMQEPi)(i=1,2)解的H\"{o}lder 连续性，并且用适当的注和例子来逐一说明各个定理的结果.最后，将混合Minty-type含参对偶向量混合拟均衡问题应用于Minty-type变分不等式.本文的结论是对其他作者的研究工作的推广和改进.

Abstract:

In this paper, following the dual rules for an equilibrium problem, we introduce the corresponding parametric dual vector mixed quasi-equilibrium problem, which is Mix Minty-type parametric dual vector quasi-equilibrium problem. We discuss the H\"{o}lder continuity of the solutions of parametric primal vector mixed quasi-equilibrium problem (PVMQEPi)(i=1,2) and parametric dual vector mixed quasi-equilibrium problem(DVMQEPi)(i=1,2) in general settings and also provide suitable remarks and examples to illustrate our results on by one. Finally, we apply Mixed Minty-type dual vector mixed quasi-equilibrium problems to deal with Mix Minty variational inequality as an application. Our results improve and extend the corresponding results announced by many others.