## 留言板

Banach空间中几乎渐近非扩张型映象的不动点的迭代逼近

 引用本文: 曾六川. Banach空间中几乎渐近非扩张型映象的不动点的迭代逼近[J]. 应用数学和力学, 2003, 24(12): 1258-1266.
ZENG Lu-chuan. Iterative Approximation of Fixed Points for Almost Asymptotically Nonexpansive Type Mappings in Banach Spaces[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1258-1266.
 Citation: ZENG Lu-chuan. Iterative Approximation of Fixed Points for Almost Asymptotically Nonexpansive Type Mappings in Banach Spaces[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1258-1266.

## Banach空间中几乎渐近非扩张型映象的不动点的迭代逼近

###### 作者简介:曾六川(1965- ),男,湖南人,教授,博士,博士生导师,已发表论文70余篇(E-mail:zenglc@hotmail.com).
• 中图分类号: O177.91

## Iterative Approximation of Fixed Points for Almost Asymptotically Nonexpansive Type Mappings in Banach Spaces

• 摘要: 在Banach空间中引入了一类新的几乎渐近非扩张型映象,概括了Banach空间中若干熟知的非线性的Lipschitz映象类与非Lipschitz映象类成特例;例如,熟知的非扩张映象类,渐近非扩张映象类与渐近非扩张型映象类.考虑了用于逼近几乎渐近非扩张型映象不动点的带误差的修改了的Ishikawa迭代序列的收敛性问题.关于Banach空间范数的S.S.Chang的不等式与H.K.Xu的不等式皆被用于做精确不动点与近似不动点间的误差估计.而且,张石生教授用于做带误差的修改了的Ishikawa迭代序列收敛性分析的方法(应用数学和力学,2001,22(1):23-31)被推广到几乎渐近非扩张型映象的情况.给出了用于求一致凸Banach空间中几乎渐近非扩张型映象不动点的带误差的修改了的Ishikawa迭代序列的新的收敛判据.并且,由该判据,立即得到了此类映象的带误差的修改了的Mann迭代序列的新的收敛判据.上述结果统一、改进与推广了张石生教授关于用带误差的修改了的Ishikawa与Mann迭代序列来逼近渐近非扩张型映象不动点方面的结果.
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##### 出版历程
• 收稿日期:  2001-07-24
• 修回日期:  2003-06-27
• 刊出日期:  2003-12-15

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