对称拟向量均衡问题的适定性

Well-posedness for symmetric vector quasi-equilibrium problems

研究实Banach空间中对称拟向量均衡问题的适定性。定义对称拟向量均衡问题的近似解序列,以此分别给出了对称拟向量均衡问题的适定性和唯一适定性概念。证明在一定条件下,对称拟向量均衡问题的适定性等价于ε→0时,ε-近似解集与解集间的Hausdorff距离的极限为零。唯一适定性则等价于解集非空且ε→0时,ε-近似解集的直径的极限为零。

Abstract.The well-posedness for Symmetric Vector Quasi-equilibrium Problems in real Banach topological vector spaces was studied. The well-posedness and uniquely well-posed for symmetric vector quasi-equilib- rium problems were defined in terms of the conception of the approximating solution sequence. It showed that under suitable conditions,the well-posedness was equivalent to the limit of the Hausdorff distance be- tween e--approximating solution set. The solution set of the symmetric vector quasi-equilibrium problems was found to be zero when ε→0. The necessary and sufficient conditions for the uniquely well-posedness was that the solution set should be nonempty,as well as the limit of the diameter of ε-approximating solu- tion set was zero when ε→0.