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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 21, Pages 3479-3485
http://dx.doi.org/10.1155/IJMMS.2005.3479

The convergence of mean value iteration for a family of maps

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

Received 3 January 2005; Revised 6 September 2005

Copyright © 2005 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 consider a mean value iteration for a family of functions, which corresponds to the Mann iteration with limn  αn0. We prove convergence results for this iteration when applied to strongly pseudocontractive or strongly accretive maps.