International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 54653, 5 pages

The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions

B. E. Rhoades1 and Ştefan M. Şoltuz2

1Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA
2“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Tiberiu Popoviciu, P.O. Box 68-1, Cluj-Napoca 400110, Romania

Received 25 January 2006; Revised 10 May 2006; Accepted 11 May 2006

Copyright © 2006 B. E. Rhoades and Ştefan M. Şoltuz. 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.


We show that the Mann and Ishikawa iterations are equivalently used to approximate fixed points of generalized contractions.