一类广义变分不等式组的隐迭代算法  

Implicit Iteration Algorithms of a Class for General Variational Inequalities System

作　　者：徐永春[1] 何欣枫[2] 何震[2] 

机构地区：[1]河北北方学院数学系,张家口075000 [2]河北大学数学与计算机学院,保定071002

出　　处：《数学学报（中文版）》2010年第4期751-758,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(60873203);河北省教育厅自然科学项目(2009103);张家口市科学技术研究与发展计划项目(0811024B-5)

摘　　要：依赖于投影映射的性质,许多学者在Hilbert空间研究了具不同映射的变分不等式组解的逼近问题,但在Banach空间的研究比较少.其主要原因是因为在Banach空间投影映射缺乏很好的性质.本文利用向阳非扩张保核映射(the sunny nonexpansiveretraction mapping)Q_K的性质,导出了一种隐迭代方法.用这一方法,本文的结果把[M.A.Noor,K.I.Noor,Projection algorithms for solving a system of generalvariational inequalities,Nonlinear Analysis,70(2009)2700-2706]的主要成果从Hilbert空间推广到了Banach空间.The approximate solution of a system for variational inequality with different mapping in Hilbert spaces was studied,based on the convergence of projection methods.But little research was done in Banach space.The primary reason was that projection mapping lacked preferably property in Banach space.In this paper,applying the property of the sunny nonexpansive retraction Q_K,we introduced the implicit iteration methods.By using these methods,the results presented in this paper extended the main results of[M.A.Noor,K.I.Noor,Projection algorithms for solving a system of general variational inequalities,Nonlinear Analysis,70（2009） 2700-2706] from Hilbert spaces to Banach space.

关 键 词：广义变分不等式组 一致光滑BANACH空间 隐迭代算法 

分 类 号：O177.91[理学—数学]