一致凸Banach空间非扩张映象带误差的Ishikawa型的三重迭代序列的收敛性

The Convergence Theorem of the Triple Ishikawa Iterative with Errors for Nonexpansive Mappings in a Uniformly Convex Banach Spaces

在一致凸Banach空间上,研究了半紧的非扩张压缩映象‖Tx-Ty‖≤‖x-y‖的Ishikawa型的三重迭代序列的收敛性问题,建立并证明了带误差的Ishikawa三重迭代逼近收敛定理,从而独特的推广了Mann和Ishikawa迭代方法,改进和发展了文献[1]-[7]的主要结果.

The convergence problem of the triple Ishikawa iterative sequence for semi-compacting nonexpensive mapping ｜｜Tx-Ty｜｜≤｜｜x-y｜｜ is studied on a uniformly convex Banach space. We establish and prove the approximation convergence theorems of triple Ishikawa iterative sequence with errors, and extend original iterative methods of Mann and Ishikawa. The results of this paper improve and develop main results in [1]-[7].