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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 4, Pages 141–172 (Mi izv597)  

Effective estimates for derivatives of inverse functions

Yu. V. Lysenko

Belarusian State University

Abstract: We use the ‘graph’ method to obtain estimates for the derivatives of any order of inverse functions in terms of those of the original functions. We construct explicit asymptotics of the estimates obtained as the order of the derivative tends to infinity. For analytic functions and functions in Gevrey's class, we obtain explicit estimates for all derivatives of the inverse functions.

DOI: https://doi.org/10.4213/im597

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English version:
Izvestiya: Mathematics, 2008, 72:4, 761–791

Bibliographic databases:

UDC: 517.9
MSC: 46G05, 46T20, 47J07, 49J53
Received: 21.12.2004
Revised: 10.05.2007

Citation: Yu. V. Lysenko, “Effective estimates for derivatives of inverse functions”, Izv. RAN. Ser. Mat., 72:4 (2008), 141–172; Izv. Math., 72:4 (2008), 761–791

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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