Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces

Shioji, Naoki; Takahashi, Wataru

doi:10.1090/S0002-9939-97-04033-1

Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
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by Naoki Shioji and Wataru Takahashi

Proc. Amer. Math. Soc. 125 (1997), 3641-3645

DOI: https://doi.org/10.1090/S0002-9939-97-04033-1

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Abstract:

In this paper, we study the convergence of the sequence defined by \[ x_0\in C , \;\; x_{n+1} = \alpha _{n}x + (1-\alpha _{n})Tx_n , \;\; n=0,1,2, \ldots ,\] where $0 \leq \alpha _n \leq 1$ and $T$ is a nonexpansive mapping from a closed convex subset of a Banach space into itself.

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