Iterative sequence for asymptotically demicontractive maps in Banach spaces

Let E be a real Banach space and T :E→E an asymptotically demicontractive and uniformly L-Lipschitzian map with F(T):={x∈E: Tx=x}≠∅ . We prove necessary and sufficient conditions for the strong convergence of the Mann iterative sequence to a fixed point of T.

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 302; no. 2; pp. 557 - 562
Main Authors Moore, Chika, Nnoli, B.V.C.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.02.2005
Elsevier
Subjects
Asymptotically hemicontractive maps
Banach spaces
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Necessary and sufficient condition
Sciences and techniques of general use
Strong convergence
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Asymptotically hemicontractive maps
Strong convergence
Banach spaces
Necessary and sufficient condition
Fix point
Mathematical analysis
Iterative method
Banach space
Hemicontractive map
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Summary:Let E be a real Banach space and T :E→E an asymptotically demicontractive and uniformly L-Lipschitzian map with F(T):={x∈E: Tx=x}≠∅ . We prove necessary and sufficient conditions for the strong convergence of the Mann iterative sequence to a fixed point of T.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2004.03.006