Comparison of fastness of the convergence among Krasnoselskij

Let E be an arbitrary real Banach space andK a nonempty, closed, convex (not necessarily bounded) subset of E. If T is a member of the class of Lipschitz, strongly pseudocontrac-tive 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. Copyright © 2006 G. V. R. Babu and K. N. V. V. Vara Prasad. This is an open access arti-cle distributed under the Creative Commons Attribution License, which permits unre-stricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1