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

Hirano, Norimichi

doi:10.1090/S0002-9939-1980-0553377-8

A proof of the mean ergodic theorem for nonexpansive mappings in Banach space
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Proc. Amer. Math. Soc. 78 (1980), 361-365 Request permission

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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