参数非凸弱广义Ky Fan不等式解映射的Lipschitz连续性  

Lipschitz Continuity for Solution Mappings of Parametric Non-convex Weak Generalized Ky Fan Inequality

作　　者：万德龙 孟旭东[1] WAN Delong;MENG Xudong(Science and Technology College of NCHU,Gongqingcheng 332020,Jiangxi Province,China)

机构地区：[1]南昌航空大学科技学院,江西共青城332020

出　　处：《吉林大学学报（理学版）》2021年第6期1387-1394,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11201216);江西省教育厅科学技术重点研究项目(批准号:GJJ181565,GJJ191614);江西省教育厅科学技术研究项目(批准号:GJJ161597).

摘　　要：在实赋范线性空间中,讨论参数非凸弱广义Ky Fan不等式解映射的Lipschitz连续性.首先,给出一类非线性泛函的概念及其基本性质;其次,在适当的假设条件下,建立非凸分离定理;最后,在解映射不具任何凸性、单调性和单值性的条件下,用分析的方法给出参数非凸弱广义Ky Fan不等式解映射Lipschitz连续的充分性定理,并举例验证定理.We discussed the Lipschitz continuity for solution mappings of parametric non-convex weak generalized Ky Fan inequality in real normed vector space.Firstly,we gave the concept of a class of nonlinear functional and its basic properties.Secondly,under appropriate assumptions,we established the non-convex separation theorem.Finally,we gave the sufficient theorem of Lipschitz continuity for the solution mappings of parametric non-convex weak generalized Ky Fan inequality under the conditions for the solution mapping without any convexity,monotonicity and univariate,and gave an example to prove the theorem.

关 键 词：LIPSCHITZ连续性 非凸分离定理 弱广义Ky Fan不等式 解映射 

分 类 号：O221.3[理学—运筹学与控制论]