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

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.

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.