We establish a discrete multivariate mean value theorem for the class of positive maximum component sign preserving functions. A constructive and combinatorial proof is given based upon a simplicial algorithm and vector labeling. Moreover, we apply this theorem to a discrete nonlinear complementarity problem and an economic equilibrium problem with indivisibilities and show the existence of sol...

If the function f : I → R is differentiable on the interval I ⊆ R , then for each x,a ∈ I, according to the mean value theorem, there exists a number c(x) belonging to the open interval determined by x and a , and there exists a real number θ (x) ∈]0,1[ such that f (x)− f (a) = (x−a) f (1) (c(x)) and f (x)− f (a) = (x−a) f (1) (a+(x−a)θ (x)) . In this paper we shall study the differentiability ...