| 广义复合隐迭代格式逼近非扩张映像公共不动点 |
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| 引用本文： | 陆爱霞,苏永福.广义复合隐迭代格式逼近非扩张映像公共不动点[J].应用泛函分析学报,2007,9(4):305-310. |
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| 作者姓名： | 陆爱霞 苏永福 |
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| 作者单位： | 1. 渤海石油职业学院,数信系,渤海,062552
2. 天津工业大学,理学院数学系,天津,300160 |
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| 摘 要： | 提出并使用如下广义复合隐迭代格式逼近非扩张映像族{Ti}Ni=1公共不动点:{xn=αnxn-1 (1-αn)Tnyn,yn=rnxn snxn-1 tnTnxn wnTnxn-1,rn sn tn wn=1,{αn},{rn},{sn},{tn},{wn}∈0,1],这里Tn=TnmodN.该文提出的广义复合隐迭代格式包含了目前多种迭代格式,因此,所得强弱收敛定理推广及发展了Mann,Ishikawa,XuandOri,等许多作者的结果.
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| 关 键 词： | 复合隐格式迭代 非扩张映像 强弱收敛 Opial's条件 次闭原理 |
| 文章编号： | 1009-1327(2007)04-0305-06 |
| 修稿时间： | 2006年7月10日 |
General Composite Implicit Iteration Processes for Common Fixed Points of a Finite Family of Nonexpansive Mappings |
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| LU Ai-xia,SU Yong-fu.General Composite Implicit Iteration Processes for Common Fixed Points of a Finite Family of Nonexpansive Mappings[J].Acta Analysis Functionalis Applicata,2007,9(4):305-310. |
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| Authors: | LU Ai-xia SU Yong-fu |
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| Abstract: | The purpose of this paper is to introduce the following general composite implicit iteration schemes:{ xn = αnxn-1 + (1 - αn)Tnyn,yn = rnxn + snxn-1 + tnTnxn + wnTnxn-1,rn + sn + tn + wn= 1,{αn},{rn},{sn},{tn},{wn} ∈ 0,1],where Tn = Tn mod N, for common fixed points of a finite family of nonexpansive mappings {Ti}iN=1 in Banach spaces, and to prove weak and strong convergence theorems. The general composite implicit iteration scheme presented in this paper included various concrete iteration schemes. Hence , the results presented in this paper extend, generalize and improve the results of Mann, Ishikawa, Xu and Ori, and other authors. |
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| Keywords: | composite implicit iterative nonexpansive mapping weak converges strongconverges opial's condition demi-closed principle |
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