关于增生算子方程解的Ishikawa迭代逼近

Ishikawa Iterative Approximations of Solutions to Equations Involving Accretive Operators

中文关键词:  任意实Banach空间  增生算子  带误差的Ishikawa迭代序列  收敛率估计

英文关键词:arbitrary real Banach space  accretive operator  Ishikawa iterative sequence with errors  convergence rate estimate

中文摘要:

      设X是任意实Banach空间,T:X→X是Lipschitz连续的增生算子.本文证明了,带误差的Ishikawa迭代序列强收敛到方程x+Tx=f的唯一解.而且,还给Ishikawa迭代序列提供了一般的收敛率估计.利用该结果,本文推得,若T:X→X是Lipschitz连续的强增生算子,则带误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解.

英文摘要:

      Let X be an arbitrary real Banach space and T : X →X be a Lipschitz continuous accretive operator. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation x+Tx =f. Moreover, our result provides a general convergence rate estimate for the Ishikawa iterative sequence. Utilizing this result, we show that if T : X →X is a Lipschitz continuous strongly accretive operator, then the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation Tx=f.