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

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.

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{k_n}?[1,∞),lim_n→∞ k_n=1.固定u∈C.对每个n≥1,x_n是压缩映象S_n(x) = (1 - t_n/(Lk_n))u + t_n/(Lk_n) 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 {k_n}?[1, ∞), lim_n→∞ k_n= 1. Fix u ∈ C. For each n ≥ 1, x_n is a unique fixed point of the contraction S_n(x) = (1 - t_n/(Lk_n))u + t_n/(Lk_n) Tⁿx ?x ∈ C, where {t_n}?[0, 1).Under suitable conditions, the strong convergence of the sequence{x_n}to a fixed point of T is characterized.