非线性增生算子方程带误差的三重迭代及其收敛性分析  

Three-step Iterations with Errors for Nonlinear Operator Equations and Convergence Analysis

作　　者：赵芬[1,2] 何震[1] 

机构地区：[1]河北大学数学与计算机学院 [2]石家庄机械化步兵学院基础部,河北石家庄050083

出　　处：《应用泛函分析学报》2006年第2期164-170,共7页Acta Analysis Functionalis Applicata

摘　　要：设Z为实一致光滑Banach空间,T∶Z→Z为强增生映射,文章提出了新的带误差的三重迭代序列,并证明了带误差的三重迭代序列强收敛到方程Tx=f的唯一解,(带误差的)Mann迭代和(带误差的)Ishikawa迭代均可作为其特例.此外,相关结果也讨论了关于强伪压缩映射不动点的三重迭代逼近问题.Let Z be a real uniform smooth Banach spaces, and T ： Z→Z be a strongly accretive operator. In this paper, we suggest and prove that the three-step iterative sequences with errors converges strongly to the unique solution of the equation Tx = f. This new iterative scheme imludes Mann interation and Ishikawa interation as special cases. Morcover, a related result also disscusses the three-step interative sequences approximation problem of fixed point of strongly pseudo contrattive mappings in Z.

关 键 词：三重迭代 强增生映射 强伪压缩映射 非线性增生算子 收敛性 误差 

分 类 号：O177.91[理学—数学]