曾六川.Banach空间中强增生算子的非线性方程的解的迭代构造(英文)[J].数学研究及应用,1998,18(3):329~334
Banach空间中强增生算子的非线性方程的解的迭代构造(英文)
Iterative Construction of Solutions to Nonlinear Equations of Strongly Accretive Operators in Banach Spaces
投稿时间:1994-05-28  
DOI:10.3770/j.issn:1000-341X.1998.03.003
中文关键词:  
英文关键词:strongly accretive  strictly pseudocontractive  p -uniformly smooth Banach space.
基金项目:
作者单位
曾六川 上海师范大学数学系
复旦大学数学研究所 
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中文摘要:
      本文研究p一致光滑Banach空间X中Ishikawa迭代法.受Deng与Tan,Xu的启发,证明了,当T是从X到自身的Lipschitz强增生算子时,Ishikawa迭代法强收敛到方程Tx=f的唯一解;当T是从X的有界闭凸子集到自身的Lipschitz严格伪压缩映象时,Ishikawa迭代法强收敛到T的唯一不动点.通过去掉限制limn→∞β=0或limn→∞α=limn→∞β=0,结果改进与推广了Tan,Xu的定理4.1与定理4.2,也把Deng的定理1与定理2推广到了p一致光滑Banach空间的背景.
英文摘要:
      In this paper, we investigate the Ishikawa iteration process in a p -uniformly smooth Banach space X . Motivated by Deng and Tan and Xu , we prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator from X to X , or to the unique fixed point of T when T is a Lipschitzian and strictly pseudo contractive mapping from a bounded closed convex subset C of X into itself . Our results improve and extend Theorem 4. 1 and 4. 2 of Tan and Xu by removing the restrion in their theorems. These also extend Theorems 1 and 2 of Deng to the p - uniformly smooth Banach space setting.
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