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Strong Convergence of Approximating Fixed Point Sequences for Nonexpansive Mappings

Published online by Cambridge University Press:  17 April 2009

Hong-Kun Xu
Hong-Kun Xu
Affiliation:
School of Mathematical SciencesUniversity of KwaZulu-NatalWestville CampusPrivate Bag X54001Durban 4000South Africa e-mail: xuhk@ukzn.ac.za
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Consider a nonexpansive self-mapping T of a bounded closed convex subset of a Banach space. Banach's contraction principle guarantees the existence of approximating fixed point sequences for T. However such sequences may not be strongly convergent, in general, even in a Hilbert space. It is shown in this paper that in a real smooth and uniformly convex Banach space, appropriately constructed approximating fixed point sequences can be strongly convergent.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 143 - 151
Copyright
Copyright © Australian Mathematical Society 2006

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