International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 42, Pages 2645-2651

The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators

B. E. Rhoades1 and Ştefan M. Şoltuz2

1Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA
2“T. Popoviciu” Institute of Numerical Analysis, P.O. Box 68-1, Cluj-Napoca 3400, Romania

Received 25 November 2002

Copyright © 2003 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 convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.