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

 

Approximation of fixed points of strictly pseudocontractive mappings on arbitrary closed, convex sets in a Banach space


Authors: K. P. R. Sastry and G. V. R. Babu
Journal: Proc. Amer. Math. Soc. 128 (2000), 2907-2909
MSC (1991): Primary 47H17
Published electronically: March 2, 2000
MathSciNet review: 1664363
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Abstract:

We show that any fixed point of a Lipschitzian, strictly pseudocontractive mapping $T$ on a closed, convex subset $K$ of a Banach space $X$ is necessarily unique, and may be norm approximated by an iterative procedure. Our argument provides a convergence rate estimate and removes the boundedness assumption on $K$, generalizing theorems of Liu.


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Additional Information

K. P. R. Sastry
Affiliation: Department of Mathematics, Andhra University, Visakhapatnam 530 003, India

G. V. R. Babu
Affiliation: Department of Mathematics, Andhra University, Visakhapatnam 530 003, India

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05362-4
PII: S 0002-9939(00)05362-4
Keywords: Banach space, Lipschitzian mapping, strictly pseudocontractive mapping, fixing points
Received by editor(s): May 4, 1998
Received by editor(s) in revised form: November 2, 1998
Published electronically: March 2, 2000
Additional Notes: This research was supported by UGC, India, Grant No. U4/4997/97-98.
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society