广义Lipschitz伪压缩映射黏滞迭代逼近方法的强收敛 |
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引用本文: | 宋义生,柴新宽. 广义Lipschitz伪压缩映射黏滞迭代逼近方法的强收敛[J]. 数学学报, 2008, 51(3): 501-508. DOI: CNKI:SUN:SXXB.0.2008-03-012 |
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作者姓名: | 宋义生 柴新宽 |
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作者单位: | 河南师范大学数学与信息科学学院,河南师范大学数学与信息科学学院 新乡 453007,新乡 453007 |
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摘 要: | K是Banach空间E的一个非空闭凸子集,T:K→K是一个广义Lipschitz伪压缩映射.对Lipschitz强伪压缩映射f:K→K和x_1∈K,序列{x_n}由下式定义:x_n+1=(1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.在{α_n}与{β_n}满足合适条件的情况下,每当{z∈K;μ_n‖x_n-z‖~2=inf_(y∈K)μ_n‖x_n-y‖~2}∩F(T)≠φ时,{x_n}强收敛到T的某个不动点x~*.
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关 键 词: | 广义Lipschitz伪压缩映射 黏滞迭代逼近 Banach极限 强收敛 |
收稿时间: | 2007-04-04 |
Strong Convergence Theorems of Viscosity Approximation Methods for Generalized Lipschitz Pseudocontractiive Mappings |
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Affiliation: | Yi Sheng SONG Xin Kuan CHAI College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,P.R.China |
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Abstract: | Let K be a nonempty closed convex subset of Banach space E,and T : K→K be a generalized Lipschitz pseudocontractive mapping.For any fixed Lipschitz strong pseudocontractive reaping f:K→K,the sequence {x_n} is given by:For x_1∈K,x_(n+1)= (1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.It is shown,under appropriate conditions on the sequences of real numbers {α_n} and {β_n},that {x_n} strongly converges to some fixed point x~* of T whenever {z∈K;μ_n||x_n-z||~2=inf_(y∈Kμ_n)||x_n-y||~2}∩F(T)≠0. |
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Keywords: | generalized Lipschitz pseudocontractions viscosity approximations Banach limits strong convergence |
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