| 筵丽霞,周海云.增生算子粘性逼近的强收敛定理[J].数学研究及应用,2008,28(3):579~588 |
| 增生算子粘性逼近的强收敛定理 |
| Strong Convergence Theorems of Viscosity Approximation for Accretive Operators |
| 投稿时间：2006-06-02 修订日期：2006-08-28 |
| DOI：10.3770/j.issn:1000-341X.2008.03.017 |
| 中文关键词: 不动点 非扩张映像 $m$-增生算子 粘性逼近 弱连续对偶映像 一致光滑Banach空间. |
| 英文关键词:fixed point nonexpansive mapping $m$-accretive operator viscosity approximation weakly continuous duality map uniformly smooth Banach space. |
| 基金项目:国家自然科学基金(No.10771050). |
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| 摘要点击次数: 2998 |
| 全文下载次数: 1954 |
| 中文摘要: |
| 假设$E$为实Banach空间, $A$为具有零点的增生算子. 定义序列 $\{x_n\}$如下: $x_{n+1}=\alpha_n f(x_n)+(1-\alpha_n)J_{r_n}x_n$, 这里$\{\alpha_n\}$, $\{r_n\}$ 满足一定条件的序列, 令$J_r=(I+rA)^{-1}$, $r>1$. 假如空间$E$有弱连续对偶映像,或者$E$为一致光滑的,均得到了序列 $\{x_n\}$的强收敛性结果. |
| 英文摘要: |
| Let $E$ be a real Banach space and let $A$ be an $m$-accretive operator with a zero. Define a sequence $\{x_n\}$ as follows: $x_{n+1}=\alpha_n f(x_n)+(1-\alpha_n)J_{r_n}x_n$, where $\{\alpha_n\}$, $\{r_n\}$ are sequences satisfying certain conditions, and $J_r$ denotes the resolvent $(I+rA)^{-1}$ for $r>1$. Strong convergence of the algorithm $\{x_n\}$ is obtained provided that $E$ either has a weakly continuous duality map or is uniformly smooth. |
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