Higher order directional derivatives for nonsmooth functions (Q2762969)

The authors of the paper under consideration propose a definition of higher order lower and upper directional derivatives of a real valued function \(f\) defined on a real normed space. It is proved that if \(f\) is respectable times Fréchet differentiable then these derivatives coincide with the corresponding higher order lower derivatives. A class of convex functions is characterized in Theorem 3. Theorem 4 deals with second order Taylor expansion for Fréchet differentiable functions.