一致L-Lipschitz的渐近伪压缩映象不动点的Ishikawa迭代逼近问题

在任意实的Banach空间中研究了用具误差的修正的Ishikawa与Mann迭代程序来逼近一致L-Lipschitz的渐近伪压缩映象不动点的强收敛性问题,在去掉条件$$\sum\limits_{n=0}^{\infty}\alpha_{n}^{2}<\infty, \q \sum\limits_{n=0}^{\infty }\gamma_{n}<\infty,\q \sum\limits_{n=0}^{\infty }\alpha_{n}(\beta_{n}+\delta_{n})<\infty,\q \sum\limits_{n=0}^{\infty}\alpha_{n}(k_{n}-1)<\infty$$之下,证明了相关文献的结果仍然成立.所得结果不但改进和推广了最近一些人的最新结果,而且也从根本上改进了定理的证明方法.

ITERATIVE APPROXIMATION PROBLEM OF FIXED POINTS FOR UNIFORMLY L-LIPSCHITZ AND ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS

The purpose of this paper is to investigate the strong convergence of the modified Ishikawa and Mann iterative processes with errors for approximating fixed points of uniformly L-Lipschitz and asymptotically pseudocontractive mappings in an arbitrary real Banach space. By removing the restriction $$\sum\limits_{n=0}^{\infty}\alpha_{n}^{2}<\infty,\q \sum\limits_{n=0}^{\infty}\gamma_{n}<\infty, \q \sum\limits_{n=0}^{\infty}\alpha_{n}(\beta_{n}+\delta_{n})<\infty,\q \sum\limits_{n=0}^{\infty}\alpha_{n}(k_{n}-1)<\infty,$$it is proven that the relevant results remain true. The results presented in this paper improve and extend some recent existing results.