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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A proof of the mean ergodic theorem for nonexpansive mappings in Banach space


Author: Norimichi Hirano
Journal: Proc. Amer. Math. Soc. 78 (1980), 361-365
MSC: Primary 47H09; Secondary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1980-0553377-8
MathSciNet review: 553377
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Abstract: Let C be a closed convex subset of a uniformly convex Banach space. Let $ T:C \to C$ be a nonexpansive mapping. In this paper, we deal with the weak convergence of the arithmetical means of the sequence $ {T^n}x$, and give a new proof of the mean ergodic theorem for nonexpansive mappings.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0553377-8
Keywords: Nonexpansive mapping, fixed point theorem
Article copyright: © Copyright 1980 American Mathematical Society