Banach空间中一类变分包含解的存在性和唯一性  

Existence and uniqueness of solutions for a class of variational inclusion problem in Banach spaces

作　　者：高雷阜[1] 王金希[1] 吴洪涛 

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000 [2]阜新矿业集团供电处,辽宁阜新123000

出　　处：《辽宁工程技术大学学报（自然科学版）》2012年第2期252-255,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：教育部高校博士学科点专项科研基金资助项目(20102121110002)

摘　　要：为了解决Banach空间中一类变分不等式的包含解问题,给出了正规对偶映射、k强增生映射、次微分的概念,利用强增生映射性质证明了复合型映射的强增生性,并证明了对偶空间中,变分包含问题的不动点的存在性.利用一般的对偶原理和不动点理论,证明了自反Banach空间中,满足G teaux微分和k-强增生映射的某一类变分不等式包含解的存在性和唯一性.该结果将许多相关文献中的变分包含问题由"光滑的Banach空间"推广到"自反的Banach空间",扩大了变分不等式包含解问题应用范围.In order to solve a class of variational inclusion problem in Banach spaces,the definition of normalized duality mapping,k-strongly accretive mapping,and order differential are given in this paper.Using the properties of k-strongly accretive,the authors prove that the compound mapping is strongly accretive,and also prove the existence of fixed point of variational inclusion problem in dual space.In addition,the authors use general duality principle and fixed point theory to prove that the existence and uniqueness of solutions for the class of variational inclusion problem,which satisfies Gteaux differential and k-Strongly accretive mapping.This study result generalizes variational inclusion problem from 'smooth Banach spaces' into 'reflexive Banach spaces',and extends the application range of variational inclusion problem.

关 键 词：变分不等式 对偶空间 微分 不动点 次微分 k-强增生映射 正规对偶映射 变分包含 

分 类 号：O177.91[理学—数学]