%0 Journal Article
%T Viscosity Approximation for Nonexpansive Nonself-Mappings InReflexive Banach Spaces<br>自反Banach空间中非扩张非自映射的粘滞迭代逼近方法
%A Song Yisheng
%A Li Qingchun
%A <br>宋义生
%A 李庆春
%J 系统科学与数学
%D 2007
%I 
%X Let $E$ be a reflexive and strictly convex Banach space with a uniformly G\^ateaux differentiable norm, and $K$ be a nonempty closed convex subset of $E$ which is also a sunny nonexpansive retract of $E$. Assume that $T:K\to E$ is a nonexpansive mapping with $F(T)\neq\emptyset$, and $f:K\to K$ is a fixed contractive mapping. The implicit iterative sequence $\{x_t\}$ is defined by $x_t=P(tf(x_t)+(1-t)Tx_t)$ for $t\in (0,1).$ The explicit iterative sequence$\{x_n\}$ is given by $x_{n+1}=P(\alpha_nf(x_n)+(1-\alpha_n)Tx_n)$, where $\alpha_n\in(0,1)$ satisfies appropriate conditions and $P$ is nonexpansive retraction of $E$ onto $K$. It is shown that $\{x_t\}$ and $\{x_n\}$ strongly converges to a fixed point of $T$.
%K Nonexpansive nonself-mappings
%K viscosity approximation
%K strictly convex Banach space<br>非扩张非自映射
%K 粘滞迭代方法
%K 严格凸的Banach空间
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=D5DD93C53810568BC193BB129454DF53&yid=A732AF04DDA03BB3&vid=DB817633AA4F79B9&iid=E158A972A605785F&sid=283B38DAD0D068F3&eid=036D726259190A01&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=15