| 非扩张映象不动点的黏性逼近 |
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| 引用本文： | 刘玉军,霍曙明.非扩张映象不动点的黏性逼近[J].安阳师范学院学报,2010(2):1-3. |
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| 作者姓名： | 刘玉军 霍曙明 |
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| 作者单位： | 1. 安阳师范学院,数学与统计学院,河南,安阳,455002
2. 安阳市高级技工学校,河南,安阳,455002 |
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| 基金项目： | 河南省教育厅自然科学研究项目 |
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| 摘 要： | 设C是一致光滑Banach空间X的一个闭凸子集,T：C→C是非扩张映象且不动点集F（T）≠Φ,f：C→C是一个固定的压缩映射.序列{xn}由下式定义：xn＋1=αnf（xn）＋（1-αn）（βnxn＋（1-βn）Txn）其中αn,βn∈（0,1）.当αn和βn满足一定条件时,则序列{xn}强收敛到T的不动点.
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| 关 键 词： | 不动点 非扩张映象 强收敛 一致光滑 |
Viscosity Approximation Fixed Points For Nonexpansive Mapping |
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| LIU Yu-jun,HUO Shu-ming.Viscosity Approximation Fixed Points For Nonexpansive Mapping[J].Journal of Aayang Teachers College,2010(2):1-3. |
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| Authors: | LIU Yu-jun HUO Shu-ming |
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| Institution: | LIU Yu-jun 1,HUO Shu-ming 2(1.School of Mathematics and statistics,Anyang Normal University,Anyang 455002,China;2.Anyang Advanced Technical Training School,Anyang 455002,China) |
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| Abstract: | Let C be a closed convex subset of a uniformly smooth Banach space X,and T:C→C is a non-expansive mapping such that,and be a fixed contractive mapping.The sequence is given by:xn+1=αnf(xn)+(1-αn)(βnxn+(1-βn)Txn) where αn,βn∈(0,1).We prove that{xn}strongly converges to a fixed point of T as αn,βn satisfying some appropriate conditions. |
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| Keywords: | Fixed point Nonexpansive mapping Strong convergence Uniformly smooth |
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