Open Access
1999/2000 C{k,1} Functions and Riemann Derivatives
Davide La Torre, Matteo Rocca
Real Anal. Exchange 25(2): 743-752 (1999/2000).


In this work we provide a characterization of $C^{k,1}$ functions of one real variable (that is, $k$ times differentiable with locally Lipschitz $k$-th derivative) 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. "C{k,1} Functions and Riemann Derivatives." Real Anal. Exchange 25 (2) 743 - 752, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 3 January 2009

zbMATH: 1016.26007
MathSciNet: MR1778527

Primary: 26A16 , 26A24

Keywords: divided differences , Lipschitz functions , Riemann derivatives

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 2 • 1999/2000
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