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
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.
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.