This article is cited in 1 paper

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.

UDC: 517.9

MSC: 46G05, 46T20, 47J07, 49J53

Received: 21.12.2004
Revised: 10.05.2007

DOI: 10.4213/im597

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

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