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# On the Convergence of Some Iteration Processes in Uniformly Convex Banach Spaces

J. Gwinner
Proceedings of the American Mathematical Society
Vol. 71, No. 1 (Aug., 1978), pp. 29-35
DOI: 10.2307/2042210
Stable URL: http://www.jstor.org/stable/2042210
Page Count: 7
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## Abstract

For the approximation of fixed points of a nonexpansive operator $T$ in a uniformly convex Banach space $E$ the convergence of the Mann-Toeplitz iteration $x_{n + 1} = \alpha_nT(x_n) + (1 - \alpha_n)x_n$ is studied. Strong convergence is established for a special class of operators $T$. Via regularization this result can be used for general nonexpansive operators, if $E$ possesses a weakly sequentially continuous duality mapping. Furthermore strongly convergent combined regularization-iteration methods are presented.

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