Transformations which preserve convexity (Q1060309)

Let C be the class of convex nondecreasing functions \(f: [0,\infty)\to [0,\infty)\) which satisfy \(f(0)=0.\) \textit{A. W. Marshall} and \textit{F. Proschan} [Inequalities III, Proc. 3rd Symp., Los Angeles 1969, 225-234 (1972; Zbl 0301.26012)] determine the one-to-one and onto functions \(\psi: [0,\infty)\to [0,\infty)\) such that \(g=\psi \circ f\circ \psi^{- 1}\) belongs to C whenever f belongs to C. We study several natural models for multivariate extension of the Marshall-Proschan result. We show that these result in essentially a restatement of the original Marshall- Proschan characterization.