International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 54653, 5 pages
doi:10.1155/IJMMS/2006/54653

The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions

B. E. Rhoades1 and Ştefan M. Şoltuz2

 1Department of Mathematics, Indiana University, Bloomington 47405-7106, IN, USA
2“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Tiberiu Popoviciu, P.O. Box 68-1, Cluj-Napoca 400110, Romania
Received 25 January 2006; Revised 10 May 2006; Accepted 11 May 2006

Abstract

We show that the Mann and Ishikawa iterations are equivalently used to approximate fixed points of generalized contractions.