Browder-Petryshyn型严格半伪压缩映射的强收敛性

Strong Convergence for Strictly Demi-pseudocontractive Mappings of the Browder-Petryshyn Type

通过引入比严格伪压缩映射更一般的严格半伪压缩映射的概念,得到了任意实Banach空间中带误差的Ishikawa迭代法生成的序列强收敛于严格半伪压缩映射的不动点的一些充要条件;作为应用,给出了序列强收敛于不动点的一个充分条件,从而将相关结果从q-一致光滑实Banach空间延拓至任意实。Banach空间;并给出了Ishikawa迭代序列的误差估计,所用的证明方法与已有的不同且更为简单。

By introducing a concept of strictly demi-pseudocontractive mapping some sufficient and necessary conditions on the strong convergence generated from the Ishikawa iteration method with errors to fixed points of strictly demi-pseudocontractive mapping are established in arbitrary real Banach spaces, As an application, a sufficient condition on strong convergence to fixed points is given. Receipt results can thus be extended from q q-uniformly smooth real Banach spaces to arbitrary real Banach spaces~ the error estimate of Ishikawa itcrative sequence is also given.