Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 242916, 7 pages
Data Dependence for Ishikawa Iteration When Dealing with
1Departamento de Matematicas, Universidad de los Andes, Carrera 1 No. 18A-10, Bogota, Colombia
2The Institute of Numerical Analysis, P.O. Box 68-1, Cluj-Napoca, Romania
3Department of Applied Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Received 13 February 2008; Accepted 27 May 2008
Academic Editor: Hichem Ben-El-Mechaiekh
Copyright © 2008 Ş. M. Şoltuz and Teodor Grosan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove a convergence result and a data dependence for Ishikawa iteration when applied to contraction-like operators. An example is given, in which instead of computing the fixed point of an operator, we approximate the operator with a contractive-like one. For which it is possible to compute the fixed point, and therefore to approximate the fixed point of the initial operator.