Banach空间中广义混合拟变分不等式解的存在性  

Existence of solutions of generalized mixed quasi-variational inequality problem in Banach space

作　　者：郑琼悦 林惠玲[1] ZHENG Qiong-yue;LIN Hui-ling(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117

出　　处：《高校应用数学学报（A辑）》2022年第4期464-474,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：福建省自然科学基金(2021J01654)。

摘　　要：在Banach空间中,探讨广义混合拟变分不等式(简记为GMQVI)解存在的充分和必要条件.当可行集是有界闭凸集时,给出了GMQVI解存在的一个充分条件;在可行集为无界闭凸集的情况下,提出GMQVI的一个新的例外簇概念,基于此,得到了GMQVI解存在的若干充分条件和必要条件.This paper is mainly devoted to the sufficient and necessary conditions for the existence of solutions of generalized mixed quasi-variational inequalities(GMQVI for short) in Banach space.When a feasible set is a bounded closed convex set,a sufficient condition for the existence of solutions for GMQVI is given.Moreover,in the case that the feasible set is unbounded closed convex set,a new conception of exceptional family of GMQVI is proposed.Based on this conception,serveral sufficient conditions and a necessary condition for the existence of solutions of GMQVI are obtained.

关 键 词：广义混合拟变分不等式 例外簇 Leray-Schauder择一定理 广义f-投影算子 正规对偶映射 

分 类 号：O177.91[理学—数学]