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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Fixed points by mean value iterations


Author: Gordon G. Johnson
Journal: Proc. Amer. Math. Soc. 34 (1972), 193-194
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1972-0291918-4
MathSciNet review: 0291918
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Abstract: If E is a convex compact subset of a Hilbert space, T is a strictly pseudocontractive function from E into E and $ {x_1}$ is a point in E, then the point sequence $ \{ {x_1}\} _{i = 1}^\infty $ converges to a fixed point of T, where for each positive integer n,

$\displaystyle {x_{n + 1}} = [1/(n + 1)][T{x_n} + n{x_n}].$


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DOI: https://doi.org/10.1090/S0002-9939-1972-0291918-4
Article copyright: © Copyright 1972 American Mathematical Society