Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 252871, 10 pages
doi:10.1155/2010/252871
Research Article

On Equivalence of Some Iterations Convergence for Quasi-Contraction Maps in Convex Metric Spaces

Zhiqun Xue,1 Guiwen Lv,1 and B. E. Rhoades2

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

Received 23 July 2010; Accepted 9 September 2010

Academic Editor: Marlène Frigon

Copyright © 2010 Zhiqun Xue et al. 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 show the equivalence of the convergence of Picard and Krasnoselskij, Mann, and Ishikawa iterations for the quasi-contraction mappings in convex metric spaces.