Fixed Point Theory and Applications
Volume 2004 (2004), Issue 2, Pages 97-105
doi:10.1155/S1687182004311058

Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators

Vasile Berinde

Department of Mathematics and Computer Science, North University of Baia Mare, Victorie 76, Baia Mare 430072, Romania

Abstract

In the class of quasi-contractive operators satisfying Zamfirescu's conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent to the unique fixed point. In this paper, the comparison of the first two methods with respect to their convergence rate is obtained.