摘要
设X是一实Banach空间,T∶X→X是Lipschitz连续的增生算子,在没有假设∑∞n=0αnβn<∞之下,本文证明了由xn+1=(1-αn)xn+αn(f-Tyn)+un以yn=(1-βn)xn+βn(f-Txn)+vn,n≥0产生的带误差的Ishikawa迭代序列强收敛到方程x+Tx=f的唯一解,并给出了更为一般的收敛率估计:若un=vn=0,n≥0,则有‖xn+1-x*‖≤(1-αn)‖xn-x*‖≤…≤∏in=0(1-αj)‖xn-x*‖,其中{αn}是(0,1)中的序列,满足γn≥4ηL(L+1)αn,n≥0。
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∑n=0^∞αnβn〈∞, it is shown that the Ishikawa iterative sequence with errors enpendened by xn＋1=（1-αn）xn＋αn（f-Tyn）＋un and yn=（1-βn）xn＋βn（f-Txn）＋vn,for all A↓n≥0 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：If un=vn=0,for all n≥0,then we have ｜｜xn＋1-x^＊｜｜≤（1-αn）｜｜xn-x^＊｜｜≤…≤∏i=0^n（1-αj）｜｜xn-x^＊｜｜.Where{αn}is a sequence in（0,1）such that for all n≥0,γn≥η/4L（L＋1）αn.
出处
《重庆师范大学学报（自然科学版）》
CAS
2008年第2期8-11,共4页
Journal of Chongqing Normal University:Natural Science
基金
重庆市自然科学基金资助项目(No.CSTC2005BB2189)
