The theory of IPH functions defined on either the cone ℝ ++ n or the cone ℝ + n can be applied in the study of various classes of monotonic functions. One of possible approaches in this direction is to use the hypographs of decreasing functions and the epigraphs of increasing functions. Consider, for example, a decreasing upper semicontinuous function g defined on the cone ℝ ++ n . The positive part hyp + g = {(x, λ) : x ∈ ℝ ++ n , 0 < λ < g(x)} of the hypograph of this function is a closed normal subset of the cone ℝ ++ n+1 , hence there exists an IPH function p defined on ℝ ++ n+1 such that hyp + g is the support set of p with respect to the set L of all min-type functions. This observation allows us to examine decreasing functions with the help of IPH functions (See Section 3.4).