Open Access

Approximating Fixed Points of Nonexpansive Mappings in Hyperspaces

Fixed Point Theory and Applications20082007:050596

DOI: 10.1155/2007/50596

Received: 29 March 2007

Accepted: 13 September 2007

Published: 20 January 2008

Abstract

Two convergence theorems for the Ishikawa and Mann iteration sequences involving nonexpansive mappings in hyperspaces are established.

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Authors’ Affiliations

(1)
Department of Mathematics, Liaoning Normal University
(2)
Department of Science, Dalian Fisheries College
(3)
Department of Mathematics and the Research Institute of Natural Science, Gyeongsang National University
(4)
Department of Applied Mathematics, Changwon National University

References

  1. Hu T, Huang J: Iteration of fixed points on hyperspaces. Chinese Annals of Mathematics. Series B 1997,18(4):423–428.MATHMathSciNetGoogle Scholar
  2. Deng L: Convergence of the Ishikawa iteration process for nonexpansive mappings. Journal of Mathematical Analysis and Applications 1996,199(3):769–775. 10.1006/jmaa.1996.0174MATHMathSciNetView ArticleGoogle Scholar
  3. Emmanuele G: Convergence of the Mann-Ishikawa iterative process for nonexpansive mappings. Nonlinear Analysis: Theory, Methods & Applications 1982,6(10):1135–1141. 10.1016/0362-546X(82)90079-7MATHMathSciNetView ArticleGoogle Scholar
  4. Ishikawa S: Fixed points and iteration of a nonexpansive mapping in a Banach space. Proceedings of the American Mathematical Society 1976,59(1):65–71. 10.1090/S0002-9939-1976-0412909-XMATHMathSciNetView ArticleGoogle Scholar
  5. Maiti M, Ghosh MK: Approximating fixed points by Ishikawa iterates. Bulletin of the Australian Mathematical Society 1989,40(1):113–117. 10.1017/S0004972700003555MATHMathSciNetView ArticleGoogle Scholar
  6. Rhoades BE: Some properties of Ishikawa iterates of nonexpansive mappings. Indian Journal of Pure and Applied Mathematics 1995,26(10):953–957.MATHMathSciNetGoogle Scholar
  7. Senter HF, Dotson WG Jr.: Approximating fixed points of nonexpansive mappings. Proceedings of the American Mathematical Society 1974,44(2):375–380. 10.1090/S0002-9939-1974-0346608-8MATHMathSciNetView ArticleGoogle Scholar
  8. Takahashi W, Kim G-E: Approximating fixed points of nonexpansive mappings in Banach spaces. Mathematica Japonica 1998,48(1):1–9.MATHMathSciNetGoogle Scholar
  9. Tan K-K, Xu HK: Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. Journal of Mathematical Analysis and Applications 1993,178(2):301–308. 10.1006/jmaa.1993.1309MATHMathSciNetView ArticleGoogle Scholar
  10. Xu H-K: Multivalued nonexpansive mappings in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications 2001,43(6):693–706. 10.1016/S0362-546X(99)00227-8MATHMathSciNetView ArticleGoogle Scholar
  11. Zeng L-C: A note on approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. Journal of Mathematical Analysis and Applications 1998,226(1):245–250. 10.1006/jmaa.1998.6053MATHMathSciNetView ArticleGoogle Scholar

Copyright

© Zeqing Liu et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.