Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 35704, 12 pages

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

Copyright © 2006 G. V. R. Babu and K. N. V. V. Vara Prasad. 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.


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 L1, 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.