Differentiability properties of functions that are ℓℓ-stable at a point

The class of the ℓℓ-stable functions is introduced in previous papers of the authors as a generalization of the class of C1,1C1,1 functions. The importance of this class is that minimization problems with ℓℓ-stable data admit second-order optimality conditions in terms of suitable directional derivatives similar to those for ones with C1,1C1,1 data. The present paper studies differentiability properties of ℓℓ-stable functions in normed spaces and generalizes to infinite-dimensional spaces some results of the authors.