An asymptotic bound for the iterates of certain real functions near a contractive fixed point
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- by Lawrence J. Wallen PDF
- Proc. Amer. Math. Soc. 109 (1990), 395-398 Request permission
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
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N. G. de Bruijn, Asymptotic methods in analysis, Wiley, New York, 1961.
- Vladimir Drobot and Lawrence J. Wallen, Asymptotic iteration, Math. Mag. 64 (1991), no. 3, 176–180. MR 1110745, DOI 10.2307/2691299
- A. M. Ostrowski, Solution of equations in Euclidean and Banach spaces, Pure and Applied Mathematics, Vol. 9, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. Third edition of Solution of equations and systems of equations. MR 0359306
Additional Information
- © Copyright 1990 American Mathematical Society
- 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