基于预解式的似变分不等式问题解的存在性  

Existence of the Solution for Variational-like Inequality Problem Based on the Resolvent Operator

作　　者：许岩[1] 戎卫东[1] 

机构地区：[1]内蒙古大学数学系

出　　处：《内蒙古大学学报（自然科学版）》2007年第5期498-501,共4页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助课题

摘　　要：在研究广义变分不等式问题时,方法之一是构造一系列辅助问题来逼近原问题的解,即辅助原理技术;另一种方法是借助η-次微分的概念,构造η-次微分映射的预解式来逼近问题的解,即预解式技术.介绍了在Hilbert空间中运用η-次微分映射的预解式技术和辅助原理技术结合不动点定理研究了一类似变分不等式问题的解的存在性和唯一性.When generalized variational inequality problem is studied, one method called auxiliary principle is to construct a series of auxiliary problems to approximate the original solution; another method called resolvent operator technique is to construct resolvent operator by using the concept of η-subdifferential. The existence and uniqueness of the solution of a class of variational-like inequality problems in Hilbert space are studied by using the resolvent operator technique of η-subdifferential, auxiliary principle technique and the fixed point theorem.

关 键 词：似变分不等式 Η-次微分 预解式技术 辅助原理技术 

分 类 号：O178[理学—数学]