Banach空间中Lipschitz伪压缩映射的近似不动点序列及其收敛定理(英文)  

Approximate Fixed Point Sequences and Convergence Theorems for Lipschitz Pseudocontractive Mappings in Banach Spaces

作　　者：魏利[1] 周海云[2,3] 

机构地区：[1]河北经贸大学数学与统计学学院 [2]华北电力大学数理学院 [3]军械工程学院应用数学与力学研究所,石家庄050003

出　　处：《应用泛函分析学报》2007年第1期29-39,共11页Acta Analysis Functionalis Applicata

基　　金：This work is supported by the National Natural Science Foundation of China Grant(10471003)

摘　　要：研究了Lipschitz伪压缩映射的黏滞迭代方法.设E为一致光滑Bannach空间,K为E的闭凸子集,TK→K为Lipschitz伪压缩映射且其不动点集F(T)非空,f为K上的压缩映射且t∈(0,1).若黏滞迭代路径{xt},xt=(1-t)f(xt)+tTxt且对任意初始向量x1∈K,迭代序列{xn}定义为xn+1=λnθnf(xn)+[1-λn(1+θn)]xn+λnTxn,则当t→1-和n→∞时,{xt}和{xn}都强收敛于T的不动点,同时该不动点还是一类变分不等式的解.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 fon K and t ∈ （0,1）, let {xt} be defined byx, = （1 - t）f（x1） ＋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 

分 类 号：O174.41[理学—数学]