东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2008, Vol. 29 ›› Issue (12): 1795-1798.DOI: -

• 论著 • 上一篇    下一篇

增算子的不动点定理及其迭代求法

孙涛;武力兵;段晓东;   

  1. 东北大学理学院;大连民族学院计算机学院;
  • 收稿日期:2013-06-22 修回日期:2013-06-22 出版日期:2008-12-15 发布日期:2013-06-22
  • 通讯作者: Sun, T.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(60573124);;教育部优秀青年教师资助计划项目

Fixed point theorems of increasing operator and its iterative solutions

Sun, Tao (1); Wu, Li-Bing (1); Duan, Xiao-Dong (2)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China; (2) School of Computer, Dalian Nationalities University, Dalian 116600, China
  • Received:2013-06-22 Revised:2013-06-22 Online:2008-12-15 Published:2013-06-22
  • Contact: Sun, T.
  • About author:-
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摘要： 设E是Hilbert空间,在强可测空间Lp[I,E]中得到了增算子不动点的存在性定理及其不动点的迭代求法,并给出了Lp[I,E]的共轭空间为Lq[I,E]这一重要结论.作为应用,研究了Hilbert空间上的一类非线性积分方程最大解和最小解及其单调迭代方法.

关键词: Hilbert空间, 共轭空间, 不动点, 迭代方法, 非线性积分方程

Abstract: Let E be a Hilbert space, some new theorems of existence of fixed point of increasing operator are obtained in strongly measurable space Lp [I, E ], as well as the iterative solutions to increasing operator. Moreover, we get the conclusion that the conjugate space of Lp [I, E] is Lq [I, E] and, for application, the maximal and minimal solutions to a class of nonlinear integral equations in Hilbert spaces and relevant monotone iterative technique are studied.

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