姚永红,陈汝栋.Banach空间中伪压缩映象不动点的迭代逼近[J].数学研究及应用,2008,28(1):169~176 |
Banach空间中伪压缩映象不动点的迭代逼近 |
Approximating Fixed Points of Pseudocontractive Mapping in Banach Spaces |
投稿时间:2005-09-05 修订日期:2006-04-12 |
DOI:10.3770/j.issn:1000-341X.2008.01.022 |
中文关键词: 伪压缩映象 $p$-一致凸Banach空间 具误差的Ishikawa迭代程序. |
英文关键词:pseudocontractive mappings $p$-uniformly convex Banach spaces Ishikawa iteration process with errors. |
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中文摘要: |
设$K$是一实$p$-一致凸Banach空间$E$的非空闭凸子集, $T$是$K$中一不动点集$F(T):=\{x\in K: Tx=x\}$非空的Lipschitz伪压缩自映象. 对$x_1\in K$, 设序列$\{x_n\}$由$x_{n+1}=a_nx_n+b_nTy_n+c_nu_n$, $y_n=a^{'}_nx_n+b^{'}_nTx_n+c^{'}_nv_n$,$n\geq 1$所生成, 则当$n\rightarrow \infty$时, $\|x_n-Tx_n\|\rightarrow 0$. 而且, 如果$T$是全连续的, 则$\{x_n\}$强收敛到$T$的一不动点. |
英文摘要: |
Let $K$ be a nonempty closed convex subset of a real p-uniformly convex Banach space $E$ and $T$ be a Lipschitz pseudocontractive self-mapping of $K$ with $F(T):=\{x\in K: Tx=x\}\neq \emptyset$. Let a sequence $\{x_n\}$ be generated from $x_1\in K$ by $x_{n+1}=a_nx_n+b_nTy_n+c_nu_n$, $y_n=a'_nx_n+b'_nTx_n+c^{'}_nv_n$ for all integers $n\geq 1$. Then $\|x_n-Tx_n\|\rightarrow 0$ as $n\rightarrow \infty$. Moreover, if $T$ is completely continuous, then $\{x_n\}$ converges strongly to a fixed point of $T$. |
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