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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Fixed points by a new iteration method

Author: Shiro Ishikawa
Journal: Proc. Amer. Math. Soc. 44 (1974), 147-150
MSC: Primary 47H10
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.

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PII: S 0002-9939(1974)0336469-5
Keywords: Iteration method, pseudo-contractive map
Article copyright: © Copyright 1974 American Mathematical Society