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

 

Weak convergence theorems for nonexpansive mappings and semigroups in Banach spaces with Opial's property


Author: T. Kuczumow
Journal: Proc. Amer. Math. Soc. 93 (1985), 430-432
MSC: Primary 47H20; Secondary 47H09
MathSciNet review: 773996
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Abstract: Let $ X$ be a Banach space with Opial's property, $ C$ a weakly compact subset of $ X$, $ x \in C$ and $ S$ a nonexpansive semigroup on $ C$. Then $ {\left\{ {S(t)x} \right\}_{t \geqslant 0}}$ converges weakly to a common fixed point of $ S$ iff $ S(t + h)x - S(t)x \rightharpoonup 0$ as $ t \to \infty $ for all $ h > 0$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0773996-8
PII: S 0002-9939(1985)0773996-8
Keywords: Nonexpansive mappings, nonexpansive semigroups, fixed points, Opial's property
Article copyright: © Copyright 1985 American Mathematical Society