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