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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Global iteration schemes
for strongly pseudo-contractive maps


Author: C. E. Chidume
Journal: Proc. Amer. Math. Soc. 126 (1998), 2641-2649
MSC (1991): Primary Primnary, 47H17, 47H06, 47H15
MathSciNet review: 1451791
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Abstract: Suppose $E$ is a real uniformly smooth Banach space, $K$ is a nonempty closed convex and bounded subset of $E$, and $T:K\to K$ is a strong pseudo-contraction. It is proved that if $T$ has a fixed point in $K$ then both the Mann and the Ishikawa iteration processes, for an arbitrary initial vector in $K$, converge strongly to the unique fixed $T$. No continuity assumption is necessary for this convergence. Moreover, our iteration parameters are independent of the geometry of the underlying Banach space and of any property of the operator.


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Additional Information

C. E. Chidume
Affiliation: International Centre for Theoretical Physics, 34100 Trieste, Italy
Email: chidume@ictp.trieste.it

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04322-6
PII: S 0002-9939(98)04322-6
Keywords: Strong pseudocontractions, accretive operators, uniformly smooth Banach spaces, duality map
Received by editor(s): April 22, 1996
Received by editor(s) in revised form: January 27, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society