Banach空间中几乎渐近非扩张型映象不动点的迭代逼近问题  

On the iterative approximation problem of fixed points for almost asymptotically nonexpansive type mappings in Banach spaces

作　　者：熊明[1] 王绍荣[1] 杨泽恒[1] 

机构地区：[1]大理学院数学系,大理671000

出　　处：《四川大学学报（自然科学版）》2007年第3期485-489,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：大理学院科研资金(2002X42);云南省教育厅科研基金(ky416140)

摘　　要：2003年,曾六川教授在Banach空间中引入了一类新的几乎渐近非扩张型映象,它包含了Banach空间中若干熟知的非线性Lipschitz映象类与非Lipschitz映象类成特例,并得到了此类映象的修改的具误差的Ishikawa迭代序列的新的收敛定理.上述结果统一、改进与推广了张石生教授的相关结果.本文作者去掉了相关文献中的条件:“对任意子列{xni}{xn},当‖Tni-xni‖→0时就有‖Txni-xni‖→0”后,得到了同样的结果,从而推广了已有的相关结果.In 2003, professor Zeng introduced a new class of almost asymptotically nonexpansive type mappings in Banach spaces which includes a number of known classes of nonlinear Lipschitzian mappings and non- Lipschitzian mappings in Banach spaces as special cases. Also, he proved the new convergence theorems of modified Ishikawa iterative sequences with errors for this class of mappings. The above results unify, improve and generalize professor Zhang results in literatures. In this paper, without the usually used condition： ＂For any {xni} belong to {xn}, if‖T^ni-xni‖→0, the ‖Txni-xni‖→0＂, the same results is proved. The results of this paper improve and generalize the corresponding results in literatures.

关 键 词：几乎渐近非扩张型映象 修改的具误差的Ishikawa迭代序列 不动点 

分 类 号：O177.91[理学—数学]