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

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.

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.