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

The convergence of mean value iteration for a family of maps

B. E. Rhoades1 and Ştefan M. Şoltuz2

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 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.

Abstract

We consider a mean value iteration for a family of functions, which corresponds to the Mann iteration with lim⁡n→∞  αn≠0. We prove convergence results for this iteration when applied to strongly pseudocontractive or strongly accretive maps.