## Real Analysis Exchange

### C{k,1} Functions and Riemann Derivatives

#### Abstract

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.

#### Article information

Source
Real Anal. Exchange, Volume 25, Number 2 (1999), 743-752.

Dates
First available in Project Euclid: 3 January 2009

https://projecteuclid.org/euclid.rae/1230995409

Mathematical Reviews number (MathSciNet)
MR1778527

Zentralblatt MATH identifier
1016.26007

#### Citation

La Torre, Davide; Rocca, Matteo. C { k ,1} Functions and Riemann Derivatives. Real Anal. Exchange 25 (1999), no. 2, 743--752. https://projecteuclid.org/euclid.rae/1230995409

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