谷峰.Banach空间中有限族渐进伪压缩映象的迭代程序[J].数学研究及应用,2009,29(5):864~870 |
Banach空间中有限族渐进伪压缩映象的迭代程序 |
Iterative Schemes for a Family of Finite Asymptotically Pseudocontractive Mappings in Banach Spaces |
投稿时间:2007-06-07 修订日期:2007-10-30 |
DOI:10.3770/j.issn:1000-341X.2009.05.012 |
中文关键词: 渐进不动点序列 一致渐进正则映象 渐进伪压缩映象 条件 共振点. |
英文关键词:approximated fixed point sequence uniformly asymptotically regular mapping asymptotically pseudocontractive mapping. |
基金项目:国家自然科学基金(No.10771141); 浙江省自然科学基金(No.Y605191); 黑龙江省自然科学基金(No.A0211); 浙江省教育厅自然科学基金(No.\,20051897). |
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中文摘要: |
设$E$是一个实Banach空间, $K$是$E$的一个非空闭凸的有界子集. 设$T_i:K\rightarrow K$, $i=1,2,\cdots,N$, 是 $N$ 个一致 $L$-Lipschitzian,具有序列$\{\varepsilon_n^{(i)}\}$的一致渐进正则和具有序列$\{k_n^{(i)}\}$的渐进伪压缩映象, 其中 $\{k_n^{(i)}\}$ 和$\{\varepsilon_n^{(i)}\}$, $i=1,2,\cdots,N$满足某些适当的条件. 设序列 $\{x |
英文摘要: |
Let $E$ be a real Banach space and $K$ be a nonempty closed convex and bounded subset of $E$. Let $T_i: K\rightarrow K$, $i=1,2,\ldots,N$, be $N$ uniformly $L$-Lipschitzian, uniformly asymptotically regular with sequences $\{\varepsilon_n^{(i)}\}$ and asymptotically pseudocontractive mappings with sequences $\{k_n^{(i)}\}$, where $\{k_n^{(i)}\}$ and $\{\varepsilon_n^{(i)}\}$, $i=1,2,\ldots,N$, satisfy certain mild conditions. Let a sequence $\{x_n\}$ be generated from $x_1\in K$ by $z_n:=(1-\mu_n)x_n \mu_nT_{n}^{n}x_n,\;x_{n 1}:=\lambda_n\theta_nx_1 [1-\lambda_n(1 \theta_n)]x_n \lambda_nT_{n}^nz_n $ for all integer $n\geqslant1$, where $T_{n}=T_{n({\rm mod}\,N)}$, and $\{\lambda_n\}$, $\{\theta_n\}$ and $\{\mu_n\}$ are three real sequences in $[0, 1]$ satisfying appropriate conditions. Then $||x_n-T_lx_n||\rightarrow 0$ as $n\rightarrow\infty$ for each $l\in\{1,2,\ldots,N\}$. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye$^{[1]}$, Reinermann$^{[10]}$, Rhoades$^{[11]}$ and Schu$^{[13]}$. |
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