Skip to content

Advertisement

  • Research Article
  • Open Access

Strong Convergence to Common Fixed Points of a Finite Family of Nonexpansive Mappings

Journal of Inequalities and Applications20072007:037513

https://doi.org/10.1155/2007/37513

  • Received: 24 December 2006
  • Accepted: 2 May 2007
  • Published:

Abstract

We suggest and analyze an iterative algorithm for a finite family of nonexpansive mappings . Further, we prove that the proposed iterative algorithm converges strongly to a common fixed point of .

Keywords

  • Iterative Algorithm
  • Nonexpansive Mapping
  • Strong Convergence
  • Finite Family

[1234567891011121314]

Authors’ Affiliations

(1)
Department of Information Management, Cheng Shiu University, Kaohsiung, 833, Taiwan
(2)
Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, China
(3)
Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, 804, Taiwan

References

  1. Atsushiba S, Takahashi W: Strong convergence theorems for a finite family of nonexpansive mappings and applications. Indian Journal of Mathematics 1999,41(3):435–453.MathSciNetMATHGoogle Scholar
  2. Bauschke HH: The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space. Journal of Mathematical Analysis and Applications 1996,202(1):150–159. 10.1006/jmaa.1996.0308MathSciNetView ArticleMATHGoogle Scholar
  3. Lions P-L: Approximation de points fixes de contractions. Comptes Rendus de l'Académie des Sciences. Séries A et B 1977,284(21):A1357-A1359.Google Scholar
  4. Shimizu T, Takahashi W: Strong convergence to common fixed points of families of nonexpansive mappings. Journal of Mathematical Analysis and Applications 1997,211(1):71–83. 10.1006/jmaa.1997.5398MathSciNetView ArticleMATHGoogle Scholar
  5. Takahashi W, Tamura T, Toyoda M: Approximation of common fixed points of a family of finite nonexpansive mappings in Banach spaces. Scientiae Mathematicae Japonicae 2002,56(3):475–480.MathSciNetMATHGoogle Scholar
  6. Zeng LC, Cubiotti P, Yao J-C: Approximation of common fixed points of families of nonexpansive mappings. to appear in Taiwanese Journal of Mathematics to appear in Taiwanese Journal of MathematicsGoogle Scholar
  7. Wittmann R: Approximation of fixed points of nonexpansive mappings. Archiv der Mathematik 1992,58(5):486–491. 10.1007/BF01190119MathSciNetView ArticleMATHGoogle Scholar
  8. Halpern B: Fixed points of nonexpanding maps. Bulletin of the American Mathematical Society 1967, 73: 957–961. 10.1090/S0002-9904-1967-11864-0MathSciNetView ArticleMATHGoogle Scholar
  9. Kimura Y, Takahashi W, Toyoda M: Convergence to common fixed points of a finite family of nonexpansive mappings. Archiv der Mathematik 2005,84(4):350–363. 10.1007/s00013-004-1175-zMathSciNetView ArticleMATHGoogle Scholar
  10. Xu H-K: Another control condition in an iterative method for nonexpansive mappings. Bulletin of the Australian Mathematical Society 2002,65(1):109–113. 10.1017/S0004972700020116MathSciNetView ArticleMATHGoogle Scholar
  11. Bruck RE Jr.: Properties of fixed-point sets of nonexpansive mappings in Banach spaces. Transactions of the American Mathematical Society 1973, 179: 251–262.MathSciNetView ArticleMATHGoogle Scholar
  12. Suzuki T: Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals. Journal of Mathematical Analysis and Applications 2005,305(1):227–239. 10.1016/j.jmaa.2004.11.017MathSciNetView ArticleMATHGoogle Scholar
  13. Xu H-K: Viscosity approximation methods for nonexpansive mappings. Journal of Mathematical Analysis and Applications 2004,298(1):279–291. 10.1016/j.jmaa.2004.04.059MathSciNetView ArticleMATHGoogle Scholar
  14. Takahashi W, Ueda Y: On Reich's strong convergence theorems for resolvents of accretive operators. Journal of Mathematical Analysis and Applications 1984,104(2):546–553. 10.1016/0022-247X(84)90019-2MathSciNetView ArticleMATHGoogle Scholar

Copyright

Advertisement