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

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.