Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 169062, 12 pages
doi:10.1155/2010/169062
Research Article

Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps

B. E. Rhoades1 and Zhiqun Xue2

1Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA
2Department of Mathematics and Physics, Shijiazhuang Railway University, Shijiazhuang 050043, China

Received 12 October 2010; Accepted 14 December 2010

Academic Editor: Juan J. Nieto

Copyright © 2010 B. E. Rhoades and Zhiqun Xue. 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.

Abstract

We provide sufficient conditions for Picard iteration to converge faster than Krasnoselskij, Mann, Ishikawa, or Noor iteration for quasicontractive operators. We also compare the rates of convergence between Krasnoselskij and Mann iterations for Zamfirescu operators.