Demyanov-Rubinov subdifferentials of real-valued functions

A new notion of subdifferentiability of real-valued functions called the Demyanov-Rubinov subdifferential is introduced. For convex functions this notion coincides with the classical subdifferential in the sense of convex analysis while for nonconvex functions it contains the Fréchet subdifferential as a (possibly empty) subset. In comparison with the latter the Demyanov-Rubinov subdifferential is non-trivial for a much broader class of functions.