周海云,赵烈济,郭金题.没有Lipschitz假设的φ-半压缩映象的不动点与φ-强拟增生算子方程解的逼近(英文)[J].数学研究及应用,2003,23(1):40~46
没有Lipschitz假设的φ-半压缩映象的不动点与φ-强拟增生算子方程解的逼近(英文)
Approximation of Fixed Point and Solution for φ-Hemicontraction and φ-Strongly Quasi-Accretive Operator without Lipschitz Assumption
投稿时间:1999-10-11  
DOI:10.3770/j.issn:1000-341X.2003.01.007
中文关键词:  
英文关键词:φ-strong pseudocontraction  φ-strongly accretive operator  Ishikawa iteration process  Reich's inequality.
基金项目:
作者单位
周海云 军械工程学院应用数学与力学研究所,河北,石家庄,050003 
赵烈济 庆尚国立大学数学系,韩国,晋州,660-701 
郭金题 华北石油教育学院数学系,河北,任丘,062551 
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中文摘要:
      设X为实一致光滑Banach空间,T:D(T)?X→X为φ-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φ-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.
英文摘要:
      Let X be a real uniformly smooth Banach space and let T:D(T)?X→X be φ-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 φ-strongly quasi-accretive operators.Our results extend and generalize thosecorresponding ones by Xu and Roach, Zhou and Jia and others.
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