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2001/2002 A Characterization of Ck,1 Functions
Davide La Torre, Matteo Rocca
Real Anal. Exchange 27(2): 515-534 (2001/2002).


In this work we provide a characterization of $C^{k,1}$ functions on $\mathbb{r}^n$ (that is, $k$ times differentiable with locally Lipschitzian $k$-th derivatives) by means of $(k+1)$-th divided differences and Riemann derivatives. In particular we prove that the class of $C^{k,1}$ functions is equivalent to the class of functions with bounded $(k+1)$-th divided difference. From this result we deduce a Taylor's formula for this class of functions and a characterization through Riemann derivatives.


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Davide La Torre. Matteo Rocca. "A Characterization of Ck,1 Functions." Real Anal. Exchange 27 (2) 515 - 534, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 2 June 2008

MathSciNet: MR1922666

Primary: 26A16 , 26A24

Keywords: divided differences , Lipschitz functions , mean value theorem , Riemann derivatives

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 2 • 2001/2002
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