Banach空间迭代序列的收敛性  

The Convergence of Iterative Sequence in Banach Space

作　　者：李焕[1] 赵河明[1] 董翠娟 覃晓琼 

机构地区：[1]中北大学机电工程学院,山西太原030051 [2]哈尔滨工程大学盎济管理学院,黑龙江哈尔滨150001 [3]淮海工业集团有限公司第一研究所,山西长治046012

出　　处：《数学的实践与认识》2015年第13期233-237,共5页Mathematics in Practice and Theory

摘　　要：先对相关基础知识进行了介绍说明,如拟增生类映象和压缩类映象,广义Lipschitz,两种迭代的迭代过程.然后阐述了目前已知相关结果,给出并论证了Mann迭代序列的收敛性.即在一致光滑的实Banach空间中,讨论并研究了带误差的Mann迭代逼近广义Lipschitz广义Φ-半压缩映象不动点的问题,改进和推广了现有的结果.In this paper, firstly, some related basic knowledge is lntroctucea, sucn as the mappings of quasi-accretive and contractive, generalized Lipschitz, the iterative schemes of two kinds of iterations. And then some related results that are known at present are illustrated. Meanwhile, convergence results of Mann iterative sequence are proved. In this paper, the problem that Mann iteration with errors approximate the fixed point of generalized Lipschitz generalizedφ-hemi-contractive mappings is discussed and investigated in uniformly smooth Banach space, the present results have been improved and popularized.

关 键 词：一致光滑的Banach空间 广义Lipschitz广义Φ-半压缩映象 不动点 带误差的Mann迭代 

分 类 号：O177.2[理学—数学]