International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 68369, 7 pages
doi:10.1155/IJMMS/2006/68369

The convergence of an implicit mean value iteration

B. E. Rhoades1 and Ştefan M. Şoltuz2

 1Department of Mathematics, Indiana University, Bloomington 47405-7106, IN, USA
2“Numerical Analysis and Application Theory Workgroup, Tiberiu Popoviciu Institute of Numerical Analysis,”, P.O. Box 68-1, Cluj-Napoca 400 110, Romania
Received 3 April 2006; Revised 10 May 2006; Accepted 11 May 2006

Abstract

We show the convergence of an implicit mean value iteration when applied to uniformly pseudocontractive maps. Remarks about other implicit mean value iterations are given.