对称拟向量均衡问题的适定性

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。

Well-posedness for symmetric vector quasi-equilibrium problems

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-equilibrium 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 between ε-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 solution set was zero when ε→0.