A characterization of Ck,1 functions

In this work we provide a characterization of C{k,1} functions on Rn (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 aTaylor's formula for this class of functions and a characterization through Riemann derivatives.