伪压缩映象不动点迭代的一点注记

关于伪压缩映象不动点迭代的一点注记

Let K be a nonempty bounded closed convex subset of a real reflexive Banach space E with a uniformly Gateaux differentiable norm. Let T : K → K be a uniformly continuous pseudocontractive mapping. Suppose every closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Let {λn} C (0, 1/2] be a sequence satisfying the conditions: (i) limn→∞λn = 0; (ii)Σ∞n=0 λn=∞. Let the sequence {xn} be generated from arbitrary x1 ∈ K by xn+1 = (1-λn)xn+ λnTxn -λn(xn- x1), n ≥1. Suppose limn→∞‖xn - Txn‖ = 0. Then {xn} converges strongly to a fixed point of T.

作 者： 姚永红 YAO Yong Hong   作者单位： Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China  刊 名： 数学研究与评论  ISTIC PKU 英文刊名： JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION  年，卷(期)： 2008 28(3)  分类号： O177.91  关键词： pseudocontractive mapping   fixed point   uniformly Gateaux differentiable norm   strong convergence  

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