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

 

Asymptotic behavior of iterates of nonexpansive mappings in Banach spaces with Opial's condition


Author: Giovanni Emmanuele
Journal: Proc. Amer. Math. Soc. 94 (1985), 103-109
MSC: Primary 47H10
MathSciNet review: 781065
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Abstract: We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0781065-6
PII: S 0002-9939(1985)0781065-6
Keywords: Opial's condition, nonexpansive mappings, asymptotic behavior of iterates, weak convergence of iterates, uniformly convex in every direction Banach spaces, semigroups of nonexpansive mappings, functions of asymptotically nonexpansive type, metric projection in uniformly convex Banach spaces
Article copyright: © Copyright 1985 American Mathematical Society