On the mean value theorem for semidifferentiable functions

摘要

The G-semidifferentiability concept was introduced in the reference Giannessi (J Optim Theory Appl 60:191-241, 1989) and it furnishes a general scheme for treating generalized derivatives. We prove that, in this context, it is possible to obtain a mean value theorem. By exploiting this result we deduce conditions for a function to be lipschitzian, C-decreasing or quasiconvex.