Fixed Point Theory and Applications 
Volume 2008 (2008), Article ID 242916, 7 pages
doi:10.1155/2008/242916
Research Article

Data Dependence for Ishikawa Iteration When Dealing with Contractive-Like Operators

Ş. M. Şoltuz1,2 and Teodor Grosan3

 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

Recommended by Hichem Ben-El-Mechaiekh

Abstract

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.