International Journal of Mathematics and Mathematical Sciences (Jan 1985)

Transformations which preserve convexity

  • Robert A. Fontenot,
  • Frank Proschan

DOI
https://doi.org/10.1155/S0161171285000047
Journal volume & issue
Vol. 8, no. 1
pp. 49 – 55

Abstract

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Let C be the class of convex nondecreasing functions f:[0,∞)→[0,∞) which satisfy f(0)=0. Marshall and Proschan [1] determine the one-to-one and onto functions ψ:[0,∞)→[0,∞) such that g=ψ∘f∘ψ−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.

Keywords