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连续伪压缩映射的黏滞迭代逼近方法
引用本文:陈汝栋,宋义生,周海云.连续伪压缩映射的黏滞迭代逼近方法[J].数学学报,2006,49(6):1275-127.
作者姓名:陈汝栋  宋义生  周海云
作者单位:[1]天津工业大学数学研究所,天津300160 [2]河南师范大学数学系,新乡453002 [3]石家庄工程学院数学系,石家庄050003
基金项目:国家自然科学基金资助项目(10371033;10271011)
摘    要:设K是实自反Banach空间E的一个闭凸子集,T:K→K是一个连续伪压缩映射,f:K→K是一个固定的L-Lipschitzian强伪压缩映射.对于任意的t∈(0,1),设x_t是tf+(1-t)T的唯一不动点.我们证明了如果T有不动点且有从E到E~*弱序列连续对偶映像,则当t趋于0时,{x_t}收敛于T的一个不动点.这个结果改进和推广了文4]的相应结果.

关 键 词:连续伪压缩映射  黏滞迭代方法  不动点
文章编号:0583-1431(2006)06-1275-04
收稿时间:2005-05-17
修稿时间:2005-05-172005-09-01

Viscosity Approximation Methods for Continuous Pseudocontractive Mappings
Ru Dong CHEN,Yi Sheng SONG,Hal Yun ZHOU.Viscosity Approximation Methods for Continuous Pseudocontractive Mappings[J].Acta Mathematica Sinica,2006,49(6):1275-127.
Authors:Ru Dong CHEN  Yi Sheng SONG  Hal Yun ZHOU
Institution:Institute of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. China Department of Mathematics, Henan Normal University, Xinxiang 453002, P. R. China Department of Mathematics, Shijiazhuang Mechanical Engineering College,Shijiazhuang 050003,P.R.China
Abstract:Let K be a closed convex subset of a real reflexive Banach space E,T: K→K be a continuous pseudocontractive mapping,and f:K→K be a fixed L-Lipschitzian strongly pseudocontractive mapping.For any t∈(0,1),let x_t be the unique fixed point of tf+(1-t)T.We prove that if T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E~*,then {x_t} converges to a fixed point of T as t approaches 0.The results presented extend and improve the corresponding results of 4].
Keywords:continuous pseudocontractive mapping  viscosity approximation  fixed point
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