Abstract
In this work we provide a characterization of C^(k,1) functions on R^n (that is 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 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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