Applied Mathematics and Mechanics

, Volume 24, Issue 6, pp 646–653 | Cite as

On reich's open question

  • Zhang Shi-sheng


Under more general form and more general conditions an affirmative answer to Reich's open question is given. The results presented also extend and improve some recent results of Reich, Shioji, Takahashi and Wittmann.

Key words

asymptotically nonexpansive mapping nonexpansive mapping fixed point iterative approximation 

Chinese Library Classification


2000 MR Subject Classification

47H07 47H10 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Goebel K, Kirk W A. A fixed point theorem for asymptotically nonexpansive mappings[J].Proc Amer Math Soc,1972,35(1):171–174.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Deimling K.Nonlinear Functional Analysis[M]. Berlin: Springer-Verlag, 1985.Google Scholar
  3. [3]
    Asplund E. Positivity of duality mappings[J].Bull Amer Math Soc, 1967,73,200–203.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Reich S. Some problems and results in fixed point theory[J].Contem Math,1983,21:179–187.zbMATHGoogle Scholar
  5. [5]
    Reich S. Strong convergence theorems for resolvent of accretive mappings in Banach spaces[J].J Math Anal Appl,1980,75:287–292.zbMATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Wittmann R. Approximation of fixed points of nonexpansive mappings[J].Arch Math,1992,58:486–491.zbMATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Shioji N, Takahashi W. Strong convergence of approximated sequence for nonexpansive mappings [J].Proc Amer Math Soc,1997,125(12):3641–3645zbMATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    Takahashi W. On Reich's strong convergence theorems for resolvents of accretive operators[J].J Math Anal Appl,1984,104:546–553.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Chang S S. Some problems and results in the study of nonlinear analysis[J].Nonlinear Anal TMA, 1997,30(7):4197–4208.zbMATHCrossRefGoogle Scholar
  10. [10]
    Liu L S. Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl1995,194:114–125.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Zhang Shi-sheng
    • 1
    • 2
  1. 1.Department of MathematicsYibin UniversityYibin, SichuanP. R. China
  2. 2.Department of MathematicsSichuan UniversityChengduP. R. China

Personalised recommendations