A theorem on mean-value iterations
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- by R. L. Franks and R. P. Marzec
- Proc. Amer. Math. Soc. 30 (1971), 324-326
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280656-9
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Abstract:
In this paper we consider a function which continuously maps a closed interval of the real line into itself. It is shown that a particular mean-value iterative scheme always converges to a fixed point. The result is known for functions which have a unique fixed point. This condition is not required here.References
- W. Robert Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510. MR 54846, DOI 10.1090/S0002-9939-1953-0054846-3
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 324-326
- MSC: Primary 26.54; Secondary 65.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280656-9
- MathSciNet review: 0280656