Journal of Applied Mathematics
Volume 2013 (2013), Article ID 274931, 5 pages
http://dx.doi.org/10.1155/2013/274931
Research Article

Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings

Haizhen Sun and Zhiqun Xue

Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

Received 28 December 2012; Accepted 11 June 2013

Academic Editor: D. R. Sahu

Copyright © 2013 Haizhen Sun and Zhiqun Xue. 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.

Abstract

Our aim in this paper is to illustrate that the proof of main theorem of Rhoades and Şoltuz (2003) concerning the equivalence between the convergences of Ishikawa and Mann iterations for uniformly -Lipschitzian asymptotically pseudocontractive maps is incorrect and to provide its correct version.