Second order differentiability and related topics in the Takagi Class

Abstract

In this paper we study some properties concerning the second order differentiability of the functions belonging to the Takagi class as well as the size of the sets where these properties hold. In particular, we characterize the set of points where these functions have a Taylor expansion of order two. Moreover, we also characterize when they satisfy a Stepanov condition of order two at a point. In this context, the convexity of such functions is also investigated. Finally, some interesting examples are provided.