Fixed Point Theory and Applications 
Volume 2006 (2006), Article ID 35704, 12 pages
doi:10.1155/FPTA/2006/35704

Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces

G. V. R. Babu1 and K. N. V. V. Vara Prasad2

 1Department of Mathematics, Andhra University, Visakhapatnam 530 003, India
2Department of Mathematics, Dr. L. Bullayya College, Visakhapatnam 530 013, India
Received 25 April 2006; Accepted 4 September 2006

Abstract

Let E be an arbitrary real Banach space and K a nonempty, closed, convex (not necessarily bounded) subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant L≥1, then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of T.