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An asymptotic bound for the iterates of certain real functions near a contractive fixed point


Author: Lawrence J. Wallen
Journal: Proc. Amer. Math. Soc. 109 (1990), 395-398
MSC: Primary 26A18
DOI: https://doi.org/10.1090/S0002-9939-1990-1010806-X
MathSciNet review: 1010806
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Abstract: If $ x = 0$ is a contractive fixed point for the function $ F$ , then under certain conditions, the iterates $ {F_k}(a)$ are asymptotically equal to the numbers $ {\xi _k}$ defined by $ k = \int_{{\xi _k}}^a {\frac{{du}}{{u - F(u)}}} $. Using somewhat different hypotheses, we give a more precise bound on $ {F_k}(a)/{\xi _k}$ .


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

  • [1] N. G. de Bruijn, Asymptotic methods in analysis, Wiley, New York, 1961.
  • [2] V. Drobot and L. J. Wallen, Asymptotic iteration, Math. Mag. (to appear). MR 1110745 (92c:65064)
  • [3] A. M. Ostrowski, Solutions of equations in Euclidean and Banach spaces, Academic Press, New York, 1973. MR 0359306 (50:11760)

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DOI: https://doi.org/10.1090/S0002-9939-1990-1010806-X
Article copyright: © Copyright 1990 American Mathematical Society

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