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Construction of sunny nonexpansive retractions in Banach spaces

Published online by Cambridge University Press:  17 April 2009

Tomas Dominguez Benavides ,
Genaro López Acedo  and
Hong-Kun Xu
Tomas Dominguez Benavides
Affiliation:
Departamento de Análisis, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain, e-mail: [email protected]
Genaro López Acedo
Affiliation:
Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa, e-mail: [email protected]
Hong-Kun Xu
Affiliation:
Departamento de Análisis, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain, e-mail: [email protected]
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Abstract

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Let  be a commutative family of nonexpansive self-mappings of a closed convex subset C of a uniformly smooth Banach space X such that the set of common fixed points is nonempty. It is shown that if a certain regularity condition is satisfied, then the sunny nonexpansive retraction from C to F can be constructed in an iterative way.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 1 , August 2002 , pp. 9 - 16
Copyright
Copyright © Australian Mathematical Society 2002

References

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