| Banach空间中渐近非扩张映象具误差的强收敛定理 |
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| 引用本文： | 赵良才,张石生. Banach空间中渐近非扩张映象具误差的强收敛定理[J]. 数学学报, 2008, 51(1): 99-108. DOI: CNKI:SUN:SXXB.0.2008-01-013 |
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| 作者姓名： | 赵良才 张石生 |
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| 作者单位： | [1]宜宾学院数学系,宜宾644000 [2]四川大学数学系,成都610064 |
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| 摘 要： | 设E是一实的Banach空间,其范数是一致Gteaux可微的;D是E的一非空闭凸子集,设T:D→D是具有序列{k_n}[1,∞),lim_(n→∞) k_n=1的渐近非扩张映象.本文证明了,在一定条件下,由(1.3)和(1.5)式定义的具误差的迭代序列{x_n}强收敛于T的不动点.本文结果也推广和改进了最近一些人的最新结果.
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| 关 键 词： | 不动点 渐近非扩张映象 具误差的迭代序列 |
| 文章编号： | 0583-1431（2008）01-0099-10 |
| 收稿时间： | 2006-05-16 |
| 修稿时间： | 2007-07-06 |
Strong Convergence Theorem for Asymptotically Nonexpansive Mappings with Errors in Banach Spaces |
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| Liang Cai ZHAO,Shi Sheng ZHANG. Strong Convergence Theorem for Asymptotically Nonexpansive Mappings with Errors in Banach Spaces[J]. Acta Mathematica Sinica, 2008, 51(1): 99-108. DOI: CNKI:SUN:SXXB.0.2008-01-013 |
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| Authors: | Liang Cai ZHAO Shi Sheng ZHANG |
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| Affiliation: | Liang Cai ZHAO Department of Mathematics,Yibin University,Yibin 644000,P.R.China Shi Sheng ZHANG Department of Mathematics,Yibin University,Yibin 644000,P.R.China Department of Mathematics,Sichuan University,Chengdu 610064,P.R.China |
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| Abstract: | Let E be a real Banach space with a uniformly Gteaux differentiable norm, D be a nonempty closed convex subset of E and T:D→D be an asymptotically nonexpansive mapping with a squence{k_n}[1,∞,k_n→1.It is shown that under some suitable conditions,the sequence with errors{x_n}defined by(1.3)and(1.5) converges strongly to some fixed points of T.The results presented in this paper also extend and improve some recent results. |
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| Keywords: | fixed point asymptotically nonexpansive mappings iterative scheme with errors |
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