一类向量变分不等式近似解的存在性证明  

Proof of the Existence of Approximate Solutions for a Class of Vector Variational Inequalities

作　　者：郎东山 古恒洋 LANG Dongshan;GU Hengyang(National Center for Applied Mathematics in Chongqing,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学重庆国家应用数学中心,重庆401331

出　　处：《东莞理工学院学报》2025年第1期15-18,共4页Journal of Dongguan University of Technology

基　　金：重庆师范大学科研创新基金(YKC23001);西昌学院博士启动基金(YBZ202411)。

摘　　要：基于KKM映射原理、广义线性引理和Hartman-Stampacchia定理,得到了在Banach空间中以共辐射集提出的向量变分不等式近似解有效解的存在性。另外,用修改函数的手段改进了证明方法,得到了这类向量变分不等式近似解弱有效解的存在性。这弥补了这类向量变分不等式近似解存在性证明的空白。In this paper,we propose approximate solutions for vector variational inequalities based on co-radiant sets in a Banach space.First,under the assumptions of pseudo-monotonicity and V-semi-continuity,we use a KKM mapping principle to prove the existence of weak approximate solutions for vector variational inequalities.Moreover,the proof method improves with the modified function to obtain the existence of the weak effective solution of the vector variational inequality.This fills the gap in the existence of solutions of such vector variational inequality.Next,we provide an alternative proof of the existence of weak approximate solutions using weak coercivity.Finally,by refining our proof methods,we demonstrate the existence of approximate solutions for vector variational inequalities in a more straightforward manner.In this paper,we obtain the existence of effective solutions for the approximate solution of vector variational inequality,based on the KKM mapping principle,the generalized linear lemma and Hartman-Stampacchia theorems.Moreover,the proof method improves with the modified function to obtain the existence of the weak effective solution of the vector variational inequality.This fills the gap in the existence of solutions of such vector variational inequality.

关 键 词：向量变分不等式的近似解 弱强制性 KKM映射定理 

分 类 号：O224[理学—运筹学与控制论]