摘要
在Banach空间中利用新的方法提出和分析了渐近非膨胀映象的具误差的三步迭代的收敛性问题.结论不仅包括具误差的修正的Mann和Ishikawa迭代序列作为特殊情况,而且去掉了定义域、值域的有界性假设.同时,获得了实Banach空间中收敛性定理的充分必要条件.文中的结论统一、改进和推广了一些熟知的结果.
By using a new method, the author suggests and analyzes the convergence problems of the three-step iterative sequence with errors for asymptotically nonexpansive mappings in Banach spaces. These results not only include the modified Mann and Ishikawa iterative sequences with errors as special cases, but also drop the boundedness requirement imposed on the domain and range in the recent corresponding results. Meanwhile, He obtains a necessity and sufficiency condition in real Banach spaces. The results presented in this paper generalize, improve and extend the known results.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2007年第1期6-10,共5页
Journal of Sichuan University(Natural Science Edition)
基金
浙江省教育厅科研基金(20051778
20051760)
宁波大学科研基金(XK200552)
关键词
渐近非膨胀映象
具误差的三步迭代
充分必要条件
具误差的修正的Mann和Ishikawa迭代
asymptotically nonexpansive, three-step iterative sequence with errors, necessity and sufficiency condition, modified Mann and Ishikawa iterative sequences with errors
