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. |
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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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