关于Hilbert空间中一类广义随机非线性变分不等式  

A class of generalized random nonlinear variational inequalities in Hilbert spaces

作　　者：周武[1] 

机构地区：[1]西南民族大学计算机科学与技术学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2016年第4期443-445,共3页Journal of Southwest Minzu University(Natural Science Edition)

摘　　要：介绍并研究了Hilbert空间中的Minty型广义随机非线性变分不等式问题,并在适当的条件和假设下,得到了这类广义非线性随机变分不等式和Stampacchia型广义随机非线性变分不等式的等价的结论;运用该结论,结合随机化的Banach压缩映像原理得到了关于这一类广义随机非线性变分不等式问题的一些新的随机解的存在性结果.This paper introduces and studies generalized random nonlinear Minty variational inequalities in Hilbert spaces. Under some suitable conditions, the equivalent relationship is obtained between generalized random nonlinear Minty variational inequalities and generalized random nonlinear Stampacchia variational inequalities. Using the radom Banaeh fixed point theorem, some new results of random solutions for this class of random varational inequalities in the setting of Hilbert spaces are obtained.

关 键 词：随机变分不等式 随机算子 随机不动点 存在性 

分 类 号：O177.1[理学—数学]