| 王绍荣,杨泽恒,熊明.Banach空间中非线性$\Phi$-伪压缩映象不动点的迭代逼近[J].数学研究及应用,2007,27(4):907~912 |
| Banach空间中非线性$\Phi$-伪压缩映象不动点的迭代逼近 |
| Iteration Approximation for Fixed Point of Nonlinear $\Phi$-Pseudocontractive Mappings in Banach Spaces |
| 投稿时间：2005-11-08 修订日期：2006-07-03 |
| DOI：10.3770/j.issn:1000-341X.2007.04.040 |
| 中文关键词: $\Phi$-伪压缩映象 具误差的Ishikawa迭代序列 不动点. |
| 英文关键词:$\Phi$-pseudocontractive mappings Ishikawa iteration sequence with errors fixed points. |
| 基金项目:云南省自然科学基金(2006A0089M). |
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| 中文摘要: |
| 本文研究了非线性拟$\Phi$-伪压缩映象与$\Phi$-伪压缩映象的不动点的迭代逼近问题.研究结果表明: 在任意实的Banach空间$E$中,拟$\Phi$-伪压缩映象与$\Phi$-伪压缩映象$T$~($T$不必连续)的具误差的Ishikawa与Mann迭代序列强收敛于$T$的唯一不动点.所得结果不但改进和推广了最近一些文献的相关结果,而且也改进了定理的证明方法. |
| 英文摘要: |
| This paper deals with the iteration approximation problem of fixed point for the nonlinear quasi-$\Phi$-pseudocontractive mappings and $\Phi$-pseudocontractive mappings. The results presented in this paper show that the quasi-$\Phi$-pseudocontractive mapping and $\Phi$-pseudocontractive mapping $T$~($T$ may not be continuous) of the Ishikawa and Mann iterative sequences with errors converges strongly to the unique fixed point of $T$ in an arbitrary real Banach space $E$. Our results improve and extend some recent results, and improve the methods of proof. |
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