Hilbert空间中关于松弛协强制映射的一类新的广义变分不等式组(英文)  

A New System of Generalized Variational Inequalities for Relaxed Cocoercive Mappings in Hilbert Spaces

作　　者：刘英[1] 陈永利[2] 

机构地区：[1]河北大学数学与计算机学院,河北保定071002 [2]华北电力大学科技学院,河北保定071051

出　　处：《应用数学》2009年第4期730-736,共7页Mathematica Applicata

基　　金：Supported by the Office of Education of Hebei Province(Z2009111)

摘　　要：在本文中,我们首先引入了一类新的关于松弛协强制映射的广义变分不等式组,通过用度量投影的方法,我们证明了这类广义变分不等式组解的存在性和唯一性.我们也建立了一类新的算法来逼近这一不等式组的解,本文的结果使得近期相关结果成为本文的特殊情况.In this paper, we first introduce a new system of generalized variational inequalities involving relaxed cocoercive mappings in Hilbert space. By using the projection method, we prove the existence and uniqueness of solutions for this new system of generalized variational inequalities. We also construct a new algorithm for approximating the solution of this system. The results presented in this paper extend and improve many related results.

关 键 词：松弛协强制映射 广义变分不等式组 度量投影 非扩张映射 Lipschitz-连续 迭代序列 

分 类 号：O177.91[理学—数学]