摘要
设X是一实Banach空间,且T:X→X是Lipschitz连续的增生算子.在没有假设limn→∞αn=lim n→∞βn=0之下,本文证明了,Ishikawa迭代序列强收敛到方程x+Tx=f的唯一解,而且还对Ishikawa迭代序列提供了一般的收敛率估计.利用该结果,我们推得,当T:X→X是Lipschitz连续的强增生算子时, Ishikawa迭代序列强收敛到方程Tx=f的唯一解.
Let X be an arbitrary real Banach space and T : X→ X be a Lipschitz continuous accretive operator. Under the lack of the assumption that lim n→∞αn= lim n→∞βn = 0, the
author proves that the Ishikawa iterative sequence converges strongly to the unique solution of the equation x + Tx = f. Moreover, this result provides a general convergence rate estimate for such a sequence. Utilizing this result, the author implies that if T : X → X is a Lipschitz continuous strongly accretive operator then the Ishikawa iterative sequence converges strongly to the unique solution of the equation Tx = f.
出处
《数学年刊（A辑）》
CSCD
北大核心
2003年第2期231-238,共8页
Chinese Annals of Mathematics
基金
高等学校优秀青年教师教学和科研奖励基金
国家自然科学基金(NO.19801023)
上海市教委高校科技发展基金资助的项目.
