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Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces

Authors: Naoki Shioji and Wataru Takahashi
Journal: Proc. Amer. Math. Soc. 125 (1997), 3641-3645
MSC (1991): Primary 47H09, 49M05
MathSciNet review: 1415370
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Abstract: In this paper, we study the convergence of the sequence defined by

\begin{displaymath}% x_0\in C , \;\; x_{n+1} = \alpha _{n}x + (1-\alpha _{n})Tx_n , \;\; n=0,1,2, \ldots,\end{displaymath}

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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Additional Information

Naoki Shioji
Affiliation: Faculty of Engineering, Tamagawa University, Tamagawa-Gakuen, Machida, Tokyo 194, Japan

Wataru Takahashi
Affiliation: Department of Information Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan

Keywords: Nonexpansive mappings, strong convergence, Banach limits, iteration
Received by editor(s): February 6, 1996
Received by editor(s) in revised form: July 15, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society