It is known that smoothness-type conditions have several implications on continuity and differentiability properties of real functions. When these conditions hold uniformly on an interval the implications become even stronger. The aim of this paper is to extend to higher orders the relations between uniform smoothness-type conditions and differentiability, taking into account higher order divided differences.
"Higher Order Uniform Smoothness and Differentiability of Real Functions." Real Anal. Exchange 26 (2) 657 - 668, 2000/2001.