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关于Shimoji and Takahashi一个定理的简单证明(英文) 被引量：2

A Simple Proof for a Theorem Due to Shimoji and Takahashi
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摘要 目的是在一般Banach空间中建立一个无限可数多个非扩张映像族的公共不动点的强收敛定理.使用一些新的分析技巧,尤其是Dotson引理和W映像技巧,给出了Shimoji and Takahashi的一个定理的简单证明. Applying the theory of semigroups of operators to evolution family and Banach contraction principle, we prove the existence and uniqueness of an （a） almost automorphic （pseudo almost automorphic） mild solution of the semilinear differential equation x′ （t） = A（t）x（t） ＋f（t, x（t）） in Banach space under conditions.
作者 周海云 马丙坤 谈斌
机构地区 军械工程学院基础部
出处 《应用泛函分析学报》 CSCD 2009年第4期289-293,共5页 Acta Analysis Functionalis Applicata
基金 Supported by the National Natural Science Foundation of China(10471033)
关键词 无限多个非扩张映像族 W映像 公共不动点 Dotson引理 almost automorphic pseudo almost automorphic semilinear differential equation evolution family exponentially stable
分类号 O177.2 [理学—基础数学]
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参考文献5

  • 1Shimoji K, Takahashi W. Strong convergence to common fixed points of infinite nonexpansive mappings and applications[J]. Taiwan Residents J Math,2001,(5):387-404.
  • 2Wittmann R. Approximation of fixed points of nonexpansive lnappings [J]. Arch Math, 1992, (58) : 486- 491.
  • 3Shioji N, Takahashi W. Strong convergence of approximated sequences for nonexpansive mappings in ganach spaces[J]. Proc Amer Math Soc, 1997, (125) : 3641-3645.
  • 4Reich S. Strong convergence theorems for resolvents of accretive operators in Banach spaces[J]. J Math Anal Appl, 1980,(75):287-292.
  • 5Dotson W G. An iterative process for nonlinear monotonic nonexpansive operators in Hilbert space[J]. Math Comp,1978, (32) :223-225.

同被引文献22

  • 1鲁红英,于刚.具有时滞和反馈控制的离散Leslie系统的概周期解[J].应用泛函分析学报,2013,15(1):88-96. 被引量：4
  • 2Guo Jian LIN,Rong YUAN.Pseudo Almost Periodic Solutions of a Singularly Perturbed Differential Equation with Piecewise Constant Argument[J].Acta Mathematica Sinica,English Series,2007,23(3):423-438. 被引量：5
  • 3YOSHIHIRO H.Bifurcation of Almost Periodic Solutions in Difference Equations[J].Journal of Difference Equations and Applications,2004,10(3):257-297.
  • 4MAQBUL M D.The Existence and Uniqueness of Almost Periodic Solutions for Abstract Functional Differential Equations[J].Electronic Journal of Differential Equation,2011,72:1-9.
  • 5PAUL H.B,DIAGANA T.Square-mean Almost Periodic Solutions Nonautonomous Stochastic Differential Equations[J].Electronic Journal of Differential Equations,2011,2007(17):1-10.
  • 6PAUL H B.Existence of Quadratic-mean Almost Periodic Solutions to Some Stochastic Hyperbolic Differential Equations[J].Electron Journal Differential Equations,2009,111:1-14.
  • 7FAROUK C.Quadratic-mean Pseudo Almost Periodic Solutions to Some Stochastic Differential Equations in a Hilbert Space[J].J.Appl Math.Comput,2012,40:427-443.
  • 8FU MM.,LIU Z X.Square Mean Almost Automorphic Solutions for Some Stochastic Differential Equations[J].Proc.Am.Math.Soc.,2010,138:3689-3701.
  • 9BOCHNER S.A New Approach to Almost-periodicity[J].Proc.Nat.Acad.Sci.USA,1962,48:2039-2043.
  • 10N' GUEREKATA G M.Almost Automorphic Functions and Amost Periodic Functions in Abstract Spaces[M].K1 uwer Academic/Plnum Publishers,New York-Bedin-Moscow,2001.

引证文献2

二级引证文献6

应用泛函分析学报
2009年 第4期

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