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
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.