A comparison of Picard and Mann Iterations for Quasi-Contraction Maps
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Date
2007
Authors
Olaleru, J.O
Journal Title
Journal ISSN
Volume Title
Publisher
Fixed Point Theory Journal
Abstract
For a class of quasi-contractive operators defined on an arbitrary Banach space, it has been shown that the Picard iteration technique converges faster than the Mann iteration technique. In this paper we make a comparison of the Picard and Mann iterations with respect to their convergence rate for a more general class of operators called quasi-contractions in metrizable topological vector spaces. It was observed that the Picard iteration converges faster than the Mann iteration for this class of maps. This answers the question posed by
Berinde in his paper.
Description
Staff publications
Keywords
Topological vector space , Fixed point , Quasi-contraction , Picard iteration , Research Subject Categories::MATHEMATICS
Citation
Olaleru, J.O. (2007). A Comparison of Picard and Mann Iterations for Quasi-Contraction Maps. Fixed Point Theory Journal, 8(1)1, 87-95.