A characterization of Ck,1 functions

Davide La Torre and Rocca Matteo ()
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Rocca Matteo: Department of Economics, University of Insubria, Italy

Economics and Quantitative Methods from Department of Economics, University of Insubria

Abstract: In this work we provide a characterization of Ck,1 functions on Rn (that ik K times differentiable with locally Lipschitz k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of Ck,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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Working Paper: A characterization of Ck,1 functions (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:ins:quaeco:qf0103

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