分裂平衡问题的Levitin-Polyak适定性

Levitin-Polyak Well-posedness for Split Equilibrium Problem

在Banach空间中研究分裂平衡问题在Lucchetti与Patrone意义下的Levitin-Polyak适定性。首先分别给出分裂平衡问题在Lucchetti与Patrone意义下的适定性和Levitin-Polyak型适定性的概念;然后借助分裂平衡问题近似解集的渐进行为及近似解集与解集的关系,建立分裂平衡问题在Lucchetti与Patrone意义下的Levitin-Polyak型适定性的Furi-Vignoli型等的距离刻画;最后,在适当的条件下证明分裂平衡问题在Lucchetti与Patrone意义下的适定性与解的存在唯一性等价。

In this paper,we study the Levitin-Polyak well-posedness(in the sense of Lucchetti and patrone) of the split equilibrium problem in Banach space.Firstly,the concepts of the well-posedness of split equilibrium problems in the sense of Lucchetti and patrone and the well-posedness of Levitin-Polyak type are given respectively.Then,with the help of the asymptotic behavior of the approximate solution set of the split equilibrium problem and the relationship between the approximate solution set and the solution set,the distance characterization of the split equilibrium problem is established in the sense of Levitin-Polyak type well-posed Furi-Vignoli type in the sense of Lucchetti and patrone.Finally,we prove that under suitable conditions,the well-posedness of the split equilibrium problem is equivalent to the existence and uniqueness of its solution.