对称拟向量均衡问题的适定性  

Well-posedness for symmetric vector quasi-equilibrium problems

作　　者：张程[1] 龚循华[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（理科版）》2012年第1期5-10,共6页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11061023);江西自然科学基金资助项目(2008GZS0072);江西省研究生创新专项资金自筹项目(YC09B004)

摘　　要：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.

关 键 词：对称拟向量均衡问题 近似解序列 HAUSDORFF距离 适定性 

分 类 号：O317[理学—一般力学与力学基础]