Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces
Open Access
- 25 January 2007
- journal article
- research article
- Published by Springer Science and Business Media LLC in Fixed Point Theory and Applications
- Vol. 2006 (1), 35704-13
- https://doi.org/10.1155/fpta/2006/35704
Abstract
Let "Equation missing" be an arbitrary real Banach space and "Equation missing" a nonempty, closed, convex (not necessarily bounded) subset of "Equation missing". If "Equation missing" is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant "Equation missing", 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 "Equation missing".Keywords
This publication has 5 references indexed in Scilit:
- Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operatorsFixed Point Theory and Applications, 2006
- Picard iteration converges faster than Mann iteration for a class of quasi-contractive operatorsFixed Point Theory and Applications, 2004
- APPROXIMATING FIXED POINTS OF LIPSCHITZIAN GENERALIZED PSEUDO-CONTRACTIONSPublished by World Scientific Pub Co Pte Ltd ,2002
- Nonlinear accretive and pseudo-contractive operator equations in Banach spacesNonlinear Analysis, 1998
- Nonlinear semigroups and evolution equationsJournal of the Mathematical Society of Japan, 1967