Hilbert空间中关于平衡与变分不等式问题及无限族非扩张映射的弱收敛定理(英文)  

Weak Convergence Theorems for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Spaces

作　　者：刘英[1] 

机构地区：[1]河北大学数学与计算机学院,河北保定071002

出　　处：《应用数学》2013年第2期292-299,共8页Mathematica Applicata

基　　金：Supported by the Natural Science Youth Foundation of Hebei Education Commission (2010110);the Natural Science Youth Foundation of Hebei Province (A2011201053,A2012201054);the Natural Science Youth Foundation of China (11101115)

摘　　要：本文根据外梯度方法引进一新的迭代序列来寻找三个集合的公共元素.这三个集合分别是无限个非扩张映射的公共不动点集、平衡问题的解集与所含映射为单调、Lipschitz连续的变分不等式问题的解集.所得结果提高和推广了许多作者的相应结果.In this paper,we introduce a new iterative sequence based on the extragradient method for finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings,the set of solutions of an equilibrium problem and the set of solutions of a variational inequality for a monotone Lipschitz continuous mapping.Our results improve and extend the corresponding results announced by many others.

关 键 词：不动点 变分不等式 非扩张映射 平衡问题 柯西列 

分 类 号：O177.91[理学—数学]