International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 42, Pages 2645-2651
doi:10.1155/S0161171203211418

The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators

B. E. Rhoades1 and Ştefan M. Şoltuz2

 1Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA
2“T. Popoviciu” Institute of Numerical Analysis, P.O. Box 68-1, Cluj-Napoca 3400, Romania
Received 25 November 2002

Abstract

We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.