基于改进集的统一含参广义集值均衡问题解映射的下半连续性

Lower semicontinuity of the solution maps of unified parametric generalized set-valued equilibrium problems with the improvement sets

本文研究含参广义集值均衡问题解映射的下半连续性.首先,利用改进集引进两类统一的含参广义集值均衡问题.其次,在合适的假设下,建立两类模型的标量化结果.最后,在新的假设下(不需要集值映射的单调性和解集的任何信息),用标量化方法研究本文提出的两类含参集值均衡问题解映射的下半连续性,并通过算例描述所获得的结果.

In this paper,we investigate the lower semicontinuity of solution maps for parametric generalized set-valued equilibrium problems.Firstly,we introduce two classes of unified parametric generalized set-valued equilibrium problems via improvement sets.Secondly,we establish the scalarization results of two kinds of models under the suitable assumptions.Finally,based on the new assumptions,which do not use monotonicity of set-valued maps and any information about the solution sets,we investigate the lower semicontinuity of the solution maps for the proposed two kinds of parametric generalized set-valued equilibrium problems by using the scalarization method.Some examples are provided to illustrate the obtained results.