应用泛函分析学报2007，Vol.9Issue(1)：29-39,11.
Banach空间中Lipschitz伪压缩映射的近似不动点序列及其收敛定理
Approximate Fixed Point Sequences and Convergence Theorems for Lipschitz Pseudocontractive Mappings in Banach Spaces
摘要
Abstract
In this article,viscosity approximation methods for Lipschitz pseudocontractive mappings are studied. Consider a Lipschitz pseudocontractive self-mapping T of a closed convex subset K of a Banach space E. Suppose that the set F(T) of fixed points of T is nonempty. For a contraction f on K and t ∈ (0,1),let {xt} be defined by xt = (1 - t)f(xt) + tTxt,and for any fixed element x1 ∈ K,let the iteration process {xn} be defined by xn+1 := λnθnf(xn) + [1 - λn(1 + θn)]xn + λnTxn. If E is a uniformly smooth Banach space,then it is shown that both {xt} and {xn} converges strongly to a fixed point of T which solves some variational inequality.关键词
一致光滑Banach空间/伪压缩映射/不动点/强收敛Key words
uniformly smooth Banach space/pseudocontractive mapping/fixed point/strong convergence分类
数理科学引用本文复制引用
魏利,周海云..Banach空间中Lipschitz伪压缩映射的近似不动点序列及其收敛定理[J].应用泛函分析学报,2007,9(1):29-39,11.基金项目
This work is supported by the National Natural Science Foundation of China Grant(10471003) （10471003）
