Banach空间中非线性$\Phi$-伪压缩映象不动点的迭代逼近

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.

Iteration Approximation for Fixed Point of Nonlinear $\Phi$-Pseudocontractive Mappings in Banach Spaces

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.