摘要
设 X 是一实的 Banach 空间,T : X → X 是一 Lipschitz 的增生算子。本文证明了具误差 的 Ishikawa 迭代序列强收敛到方程 x + Tx = f 的唯一解;并得一个一般的收敛估计式。 若 T : X → X 是一 Lipschitz 的强增生算子,则具误差的 Ishikawa 迭代序列强收敛到方 程 Tx = f 的唯一解。本文结果推广和发展了现有的相应结果。
Let X be an arbitrary real Banach spaces and be a Lipschitz accretive operator. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equstion. Moreover, our result provides a general convergence rate estimate for such a sequence. Utilizing this result, we imply that if be a Lipschitz strongly accretive operator. Then the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation. The results presented in this paper extend and improve the recent corresponding results.
出处
《工程数学学报》
CSCD
北大核心
2004年第6期967-972,共6页
Chinese Journal of Engineering Mathematics
基金
大理学院科研基金资助项目(2002X42).
