| Picard Approximation of Fixed Points of Nonexpansive Mappings |
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| 作者姓名： | 黄家琳 |
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| 作者单位： | Department of |
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| 摘 要： | LetXbeaBanachspaceandCbeaconvexsubsetofX .T :X→Cisanonexpansivemapping ,thatis ,Tx -Ty ≤x - y forallx ,y∈X .Now ,westudythefollowingiterativeprocessforx0 ,un∈C ,xn 1=Snxn, ( 1 )whereSn =αn0 I αn1T αn2 T2 … αnkTk γnun,andαni≥ 0 ,0 <α≤αn
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| 关 键 词： | 迭代过程 凸面空间 不放大映射 凸函数 |
Picard Approximation of Fixed Points of Nonexpansive Mappings |
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| Huang Jialin.Picard Approximation of Fixed Points of Nonexpansive Mappings[J].Journal of Southwest Jiaotong University,2003,11(2):189-191. |
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| Authors: | Huang Jialin |
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| Abstract: | Let C be a bounded convex subset in a uniformly convex Banach space X, x0, un∈C, then xn+1=Snxn, where Sn=αn0I+αn1T+αn2T2+…+αnkTk+γnun, αni≥0, 0＜α≤αn0≤b＜1, ∑ki=0αni+γn=1, and n≥1. It is proved that xn converges to a fixed point on T if T is a nonexpansive mapping. |
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| Keywords: | nonexpansive mapping uniformly convex space iteration process |
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