Fixed Point Theory and Applications 
Volume 2007 (2007), Article ID 61434, 5 pages
doi:10.1155/2007/61434
Review Article

Remarks of Equivalence among Picard, Mann, and Ishikawa Iterations in Normed Spaces

Xue Zhiqun

 Department of Mathematics and Physics, Shijiazhuang Railway Institute, Shijiazhuang 050043, China
Received 1 April 2007; Revised 16 April 2007; Accepted 21 June 2007

Recommended by J. R. L. Webb

Abstract

We show that the convergence of Picard iteration is equivalent to the convergence of Mann iteration schemes for various Zamfirescu operators. Our result extends of Soltuz (2005).