Abstract
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.
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References
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Castellani, M., Pappalardo, M. On the mean value theorem for semidifferentiable functions. J Glob Optim 46, 503–508 (2010). https://doi.org/10.1007/s10898-009-9434-y
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DOI: https://doi.org/10.1007/s10898-009-9434-y