Open Access

Note on some results for asymptotically pseudocontractive mappings and asymptotically nonexpansive mappings

Fixed Point Theory and Applications20062006:24978

https://doi.org/10.1155/FPTA/2006/24978

Received: 26 May 2006

Accepted: 13 August 2006

Published: 30 October 2006

Abstract

We discuss convergence theorems of modified Ishikawa and Mann iterative sequences with errors for asymptotically pseudocontractive and asymptotically nonexpansive mappings in Banach spaces, and the boundedness of the domain and range can be dropped, generalizing theorems of Chang.

[1234]

Authors’ Affiliations

(1)
Department of Mathematics, NanChang University

References

  1. Chang SS: Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings. Proceedings of the American Mathematical Society 2001,129(3):845–853. 10.1090/S0002-9939-00-05988-8MathSciNetView ArticleMATHGoogle Scholar
  2. Kato T: Nonlinear semigroups and evolution equations. Journal of the Mathematical Society of Japan 1967, 19: 508–520. 10.2969/jmsj/01940508MathSciNetView ArticleMATHGoogle Scholar
  3. Osilike MO, Akuchu BG: Common fixed points of a finite family of asymptotically pseudocontractive maps. Fixed Point Theory and Applications 2004,2004(2):81–88. 10.1155/S1687182004312027MathSciNetView ArticleMATHGoogle Scholar
  4. 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.1993.1309MathSciNetView ArticleMATHGoogle Scholar

Copyright

© Y. Tang and L. Liu. 2006

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.