刘英.在Banach空间关于变分不等式和相对非扩张映射的弱收敛[J].数学研究及应用,2010,30(4):716~724
在Banach空间关于变分不等式和相对非扩张映射的弱收敛
Weak Convergence of a Projection Algorithm for Variational Inequalities and Relatively Nonexpansive Mappings in a Banach Space
投稿时间:2008-05-06  最后修改时间:2008-10-06
DOI:10.3770/j.issn:1000-341X.2010.04.016
中文关键词:  相对非扩张映射  广义投影  逆强单调  弱序列连续  $P$-一致凸.
英文关键词:relatively nonexpansive mapping  generalized projection  inverse-strongly-monotone mapping  weakly sequential continuity  $p$-uniformly convexity constant.
基金项目:
作者单位
刘英 河北大学数学与计算机学院, 河北 保定 071002 
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中文摘要:
      在这篇论文中,引进了一迭代序列来逼近两个集合的公共点.这两个集合分别是相对非扩张映射的不动点集和变分不等式的解集.文章表明了这一迭代序列弱收敛到这两个集合的公共点.
英文摘要:
      In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets.
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