Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 647085, 10 pages
Research Article

Some Convergence Theorems of a Sequence in Complete Metric Spaces and Its Applications

Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt

Received 20 June 2009; Accepted 7 September 2009

Academic Editor: Tomas Dominguez Benavides

Copyright © 2010 M. A. Ahmed and F. M. Zeyada. 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.


The concept of weakly quasi-nonexpansive mappings with respect to a sequence is introduced. This concept generalizes the concept of quasi-nonexpansive mappings with respect to a sequence due to Ahmed and Zeyada (2002). Mainly, some convergence theorems are established and their applications to certain iterations are given.