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Proceedings of the American Mathematical Society

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Fixed points by a new iteration method


Author: Shiro Ishikawa
Journal: Proc. Amer. Math. Soc. 44 (1974), 147-150
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1974-0336469-5
MathSciNet review: 0336469
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Abstract: The following result is shown. If $ T$ is a lipschitzian pseudo-contractive map of a compact convex subset $ E$ of a Hilbert space into itself and $ {x_1}$ is any point in $ E$, then a certain mean value sequence defined by $ {x_{n + 1}} = {\alpha _n}T[{\beta _n}T{x_n} + (1 - {\beta _n}){x_n}] + (1 - {\alpha _n}){x_n}$ converges strongly to a fixed point of $ T$, where $ \{ {\alpha _n}\} $ and $ \{ {\beta _n}\} $ are sequences of positive numbers that satisfy some conditions.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1974-0336469-5
Keywords: Iteration method, pseudo-contractive map
Article copyright: © Copyright 1974 American Mathematical Society

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