| 渐近非扩张映射修正的Ishikawa迭代程序收敛定理 |
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| 引用本文： | 郭志荣,徐小平.渐近非扩张映射修正的Ishikawa迭代程序收敛定理[J].淮阴师范学院学报(自然科学版),2010,9(5). |
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| 作者姓名： | 郭志荣 徐小平 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 主要在E*具有KK性质等条件下证明了T存在不动点当且仅当由修正的Ishikawa迭代程序xn+1=tnTnyn+(1-tn)xn yn=snTnxn+(1-sn)xn所定义的序列{xn}弱收敛且xn-Txn→0.设C是一致凸Banach空间E的非空有界闭凸子集,T:C→C是渐近非扩张映射.
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| 关 键 词： | Banach空间 渐近非扩张映射 Ishikawa迭代 Kadec-Klee性质 |
Convergence Theorem of Modified Ishikawa Iterative Sequences for Asymptotically Nonexpansive Mappings |
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| GUO Zhi-rong,XU Xiao-ping.Convergence Theorem of Modified Ishikawa Iterative Sequences for Asymptotically Nonexpansive Mappings[J].Journal of Huaiyin Teachers College(Natrual Science Edition),2010,9(5). |
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| Authors: | GUO Zhi-rong XU Xiao-ping |
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| Abstract: | Let C be a nonempty bounded closed convex subset of uniformly convex Banach space.Let T:C→C be an asymptotically nonexpansive mapping.It is shown that under some suitable conditions such as thatE* satisfies KKproperty,Thas fixed point if and only if the modifiedIshikawaiterative sequences {xn}defined by xn+1=tnTnyn+(1-tn)xn yn=snTnxn+(1-sn)xn converges weakly and xn-Txn→0. |
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| Keywords: | Banach spaces asymptotically nonexpansive mappings Ishikawa iterative sequences Kadec-Klee property |
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