ON SOME CLASSES OF THE WEAKLY SUBDIFFERENTIAL FUNCTIONS

This work presents a theorem that any Lipschitz function is weakly subdifferentiable with x^* component of the weak subgradient is different from 0_(R^n ). This theorem is based on Kasimbeyli's nonlinear cone separation theorem. Also, we show that any positively homogeneous and continuous function is both upper and lower Lipschitz. Additionally, we show that positively homogeneous and lower semicontinuous functions are weakly subdifferentiable that the pair (x^*,c) which is a weak subgradient of a function in this case is different from (0_(R^n ),0).