广义混合变分不等式的有界性条件  

A boundedness condition for a generalized mixed variational inequality

作　　者：罗雪萍[1] LUO Xue-ping(School of Computer Science and Technology,Southwest Minzu University,Chengdu 610041,P.R.C.)

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）》2018年第6期627-631,共5页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(11701480);中国博士后科学基金项目(2018M631072);中央高校基本科研业务费专项资金项目(2018HQZZ23)

摘　　要：在自反巴拿赫空间中介绍广义混合变分不等式的一个新的有界性条件,并给出证明与例子说明此条件是一个较弱的条件.而且,此条件是更一般形式的有界性条件.基于一个确保广义混合变分不等式解集非空有界的强制条件,证明较弱的有界性条件是广义混合变分不等式解集非空有界的充分必要条件.最后,还给出具体例子证实定理的正确性.This paper aims to introduce a novel boundedness condition for a generalized mixed variational inequality in reflexive Banaeh spaees,and shows the proof and an example to explain that the condition is weaker.Moreover,the condition is a general one.Based on a covereivity condition guaranteeing the nonemptiness and boundedness of the solution set,the new boundedness condition is proved to be a sufficient and necessary one for ensuring the nonemptiness and boundedness of the solution set of the generalized mixed variational inequality in reflexive Banach spaces.

关 键 词：广义混合变分不等式 有界 f-伪单调 

分 类 号：O177.91[理学—数学]