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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 46, Pages 2443-2451
http://dx.doi.org/10.1155/S0161171204312020

The equivalence of Mann iteration and Ishikawa iteration for ψ-uniformly pseudocontractive or ψ-uniformly accretive maps

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

Received 2 December 2003

Copyright © 2004 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 Ishikawa iteration and the corresponding Mann iteration are equivalent when applied to ψ-uniformly pseudocontractive or ψ-uniformly accretive maps.