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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fixed points by mean value iterations
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by Gordon G. Johnson PDF
Proc. Amer. Math. Soc. 34 (1972), 193-194 Request permission

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, \[ {x_{n + 1}} = [1/(n + 1)][T{x_n} + n{x_n}].\]
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • 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