摘要
本文引入了一般多值向量变分不等式问题（ＧＭＶＶＩ），这推广和统一了现有的向量变分不等式．文内还引入了弱Ｃ- 伪单调映射和半连续映射的概念，在弱Ｃ- 伪单调性和半连续性的假设下，给出了（ＧＭＶＶＩ）的广义线性化引理和解的存在定理．本文的结果即使对一般向量变分不等式问题和广义向量变分不等式问题也是全新的．
In this paper, we introduce a general multi-valued vector variational inequality problem (GMVVI) which extends and unifies the existing vector variational inequalities. The concepts of weakly C-pseudomonotone mappings and hemicontinuous mappings are introduced. Generalized linearization lemma and exisence theorems of solutions for (GMVVI) are given with the assumptions of weakly C-pseudomonotonicity and hemicontinuity. These results are new even for the general vector variational inequality problem and generalized vector variational inequality problem.
出处
《应用数学学报》
CSCD
北大核心
2001年第2期284-290,共7页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金资助项目(10071037号)
关键词
半连续性
弱C-伪单调性
广义线性化引理
多值向量
变分不等式
解
存在定理
General multi-Valued vector variational inequality problem, hemicontinuity, weakly C-pseudomonotonicity, generalized linearization lemma, existence theorem of solutions
