Minty与Stampacchia向量似变分不等式  

Minty and Stampacchia vector variational-like inequality

作　　者：王庆东[1] 侯海军[1] 肖刚[2] 

机构地区：[1]商丘师范学院数学系,河南商丘476000 [2]西安电子科技大学理学院,陕西西安710071

出　　处：《安徽大学学报（自然科学版）》2008年第4期25-27,共3页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(69972036)

摘　　要：讨论两类向量似变分不等式解的关系问题,指出当定义在不变凸集上的映射是不变伪单调连续时,Minty(强)弱向量似变分不等式的解和Stampacchia(强)弱向量似变分不等式的解相同.尤其当定义在不变凸集上的矩阵映射是广义不变伪单调连续时,Minty强向量似变分不等式的解和Stampacchia向量似变分不等式的解相同.Two classes of vector variational-like inequality were investigated. Minty （strong） weak vector variational-like inequality and Stampacchia （strong） weak vector variational-like inequality had the same solution in the case that a matrix-valued function defined on invex set was a continuous invariant pseudomonotone mapping. Particularly, in the case of generalized invariant pseudomonotonicity of a matrixvalued mapping, minty weak vector varation-like inequality and Stampacchia vector variational-like inequality had the same solution.

关 键 词：向量似变分不等式 不变凸集 不变伪单调映射 

分 类 号：O178[理学—数学]