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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 42, Pages 2645-2651
http://dx.doi.org/10.1155/S0161171203211418

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

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 Hindawi Publishing Corporation. 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

We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.