非紧条件下广义集值隐向量拟变分不等式问题解的存在性  

Existence of solutions for the generalized set-valued implicit vector quasi-variational inequalities under noncompact conditions

作　　者：吴慧凌 林志 陈小龙 WU Hui-ling;LIN Zhi;CHEN Xiao-long(College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074

出　　处：《宝鸡文理学院学报（自然科学版）》2023年第1期14-18,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金项目(11271067)。

摘　　要：目的研究非紧条件下广义集值隐向量拟变分不等式解的存在性。方法与之前的大部分研究相比,放松了紧的条件,结合集值映射的上半-C-连续性以及C-凸或C-似拟凸性,利用不动点定理进行研究。结果给出了非紧条件下广义集值隐向量拟变分不等式问题解的存在性定理,并根据广义集值隐向量拟变分不等式问题与其他向量变分不等式问题的相关性,给出了相应的推论。结论非紧条件下解的存在性结果推广了之前的相关定理。Purposes—To study the existence of solutions for generalized set-valued implicit vector quasi-variational inequalities under noncompact conditions.Methods—Compared with most previous studies,the compact condition is relaxed herein,but the upper half-C-continuity and C-convexity or C-quasi convexity of set-valued mappings are combined,and the fixed point theorem is used.Results—Given are the existence theorems of solutions for generalized set-valued implicit vector quasi-variational inequalities under noncompact conditions,and so are the corresponding corollaries according to the correlation between generalized set-valued implicit vector quasi-variational inequality and other vector variational inequality problems.Conclusion—The existing results of solutions under noncompact conditions generalize the previous related theorems.

关 键 词：不动点定理 开下截口 C-似拟凸 上半-C-连续 

分 类 号：O224[理学—运筹学与控制论]