曾六川.关于渐近伪压缩映象迭代逼近的表征(英文)[J].数学研究及应用,2005,25(2):279~286
关于渐近伪压缩映象迭代逼近的表征(英文)
On Characterization of Iterative Approximation for Asymptotically Pseudocontractive Mappings
投稿时间:2002-09-16  
DOI:10.3770/j.issn:1000-341X.2005.02.009
中文关键词:  不动点  渐近伪压缩映象  一致Lipschitz映象  一致正规结构  Banach压缩原理
英文关键词:fixed point  asymptotically pseudocontractive mapping  uniform Lipschitzian mapping  uniform normal structure  Banach contraction principle.
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作者单位
曾六川 上海师范大学数学系,上海,200234 
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中文摘要:
      设C是Banach空间X的非空有界闭凸子集,T:C →C既是一致L-Lipschitz映象, L≥1,又是渐近伪压缩映象,具有序列{kn}?[1,∞),limn→∞ kn=1.固定u∈C.对每个n≥1,xn是压缩映象Sn(x) = (1 - tn/(Lkn))u + tn/(Lkn) Tn
英文摘要:
      Let C be a nonempty bounded closed convex subset of a Banach space X, and T: C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}?[1, ∞), limn→∞ kn= 1. Fix u ∈ C. For each n ≥ 1, xn is a unique fixed point of the contraction Sn(x) = (1 - tn/(Lkn))u + tn/(Lkn) Tnx ?x ∈ C, where {tn}?[0, 1).Under suitable conditions, the strong convergence of the sequence{xn}to a fixed point of T is characterized.
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