Banach空间中Mann迭代和Ishikawa迭代的等价性问题  

Equivalence problem of Mann and Ishikawa Iterations in Banach Spaces

作　　者：王双[1] 柴国庆[2] 胡长松[2] 

机构地区：[1]盐城师范学院数学科学学院,盐城224051 [2]湖北师范学院数学系,黄石435002

出　　处：《应用泛函分析学报》2010年第3期279-288,共10页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(10771175);湖北省教育厅自然科学基金(D200722002)

摘　　要：用不同于已有的方法证明了任意实Banach空间中一致Lipschitz强连接伪压缩算子在具误差的修正的Mann迭代和具误差的修正的Ishikawa迭代下收敛和稳定的等价性,其中迭代参数{β_n}仅需■β_n<k/L(L+1),这推广和改进了目前需假设■β_n=0和两迭代程序初始点的取值需相同条件下的已有结果.In this paper,we prove some equivalence theorems between convergence and stability of modified Mann and modified Ishikawa iterative sequence with errors for uniformly Lipschitz strongly successively pseudo-contractive mappings in Banach spaces by using different methods,under the condition on the iteration para-meters limsup lim sup n→∞βn〈k/L（L＋1）.Our results prove and extend the results that need lim n→∞ βn=0 and initial points of two different iteration are the same one.

关 键 词：具误差的修正的Mann迭代序列 具误差的修正的Ishikawa迭代序列 一致Lipschitz映象 强连接伪压缩算子 

分 类 号：O177.91[理学—数学]