Approximation of Fixed Point and Solution for -Hemicontraction and -Strongly Quasi-Accretive Operator without Lipschitz Assumption  

没有Lipschitz假设的-半压缩映象的不动点与-强拟增生算子方程解的逼近(英文)

作　　者：周海云[1] 赵烈济 郭金题[3] 

机构地区：[1]军械工程学院应用数学与力学研究所,河北石家庄050003 [2]庆尚国立大学数学系 [3]华北石油教育学院数学系,河北任丘062551

出　　处：《Journal of Mathematical Research and Exposition》2003年第1期40-46,共7页数学研究与评论（英文版）

摘　　要：Let X be a real uniformly smooth Banach space and let T:D(T)(?)X→Xbe (?)-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {αn}and{βn},we have proved thatthe Mann and Ishikawa iteration processes for T converge strongly to the unique fixedpoint q of T.Several related results deal with iterative solutions of nonlinear equationsinvolving (?)-strongly quasi-accretive operators.Our results extend and generalize thosecorresponding ones by Xu and Roach,Zhou and Jia and others.设X为实一致光滑Banach空间,T:D(T)■X→X为-半压缩映象且在它的不动点q处是局部有界的.本文证明了Mann迭代与Ishikawa迭代过程强收敛于T的唯一不动点q.几个相关的结果处理(?)-强拟增生算子方程的解的迭代构造.本文所得到的结果扩展并推广了Xu和Roach,Zhou和Jia等人的相应结果.

关 键 词：-strong pseudocontraction -strongly accretive operator Ishikawa iteration process Reich's inequality. 

分 类 号：O177.91[理学—数学]