Abstract and Applied Analysis
Volume 2009 (2009), Article ID 283461, 9 pages
doi:10.1155/2009/283461
Research Article

A Note on “Common Fixed Point of Multistep Noor Iteration with Errors for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings”

Satit Saejung,1,2 Suthep Suantai,2,3 and Pongsakorn Yotkaew1

1Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Chiang Mai University, Chiang Mai 50200, Thailand

Received 20 October 2009; Accepted 11 December 2009

Academic Editor: Simeon Reich

Copyright © 2009 Satit Saejung et al. 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

The purpose of this paper is to give a general and short principle for proving some convergence results of certain types of iterative sequences. A small gap in the paper by Imnang and Suantai (2009) is discussed and corrected. Finally, we prove that the generalized asymptotically quasi-nonexpansive mappings in the sense of Lan (2006) are nothing but asymptotically quasi-nonexpansive. Hence several results concerning these mappings become a special case of the known ones.