摘要
设1<P≤2,X是实P-一致光滑的Banach空间,T:X→是强增生算子.研究了用带误差的Ishikawa迭代程序:来逼近方程Tx=f解的问题,其中x0∈X,{un},{vn}是X中的有界序列,{αn},{βn}是[0,1]中的实数列.在无需假设条件αn→0之下,证明了,当T连续时,迭代序列{Xn}强收敛到方程Tx=f的唯一解.
Let 1 〈 p ≤ 2 , X be a rea lp -uniformly smooth Banachspace, and T：X→X be a strongly accretive operator. The problem of approximating solutions to theequation Tx= f by the Ishikawa iterative process with errors （xn＋1）=（1-αn）xn＋αn（f-Tyn＋yn）＋un, yn=（1-βn）xn＋βn（f-Txn＋xn）＋υn,n≥0,） is investigated, where x0∈X,{un}{υn} are bounded sequences in X, and {αn},{βn}are real sequences in [0,1 ] .Without the assumption that αn→0,it is shownthat if T is continuous then the iterative sequence {xn}converges strongly to the unique solution to the equation Tx = f.
出处
《上海师范大学学报（自然科学版）》
2005年第3期1-6,共6页
Journal of Shanghai Normal University(Natural Sciences)
基金
上海市曙光计划的资助项目(BL200404).
