Transformations which preserve convexity

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 Mar...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences
Main Authors: Robert A. Fontenot, Frank Proschan
Format: Article
Language:English
Published: Wiley 1985-01-01
Subjects:
convexity
preservation of convexity
transformations multivariate
permutation matrices.
Online Access:http://dx.doi.org/10.1155/S0161171285000047
Description
Summary: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.
ISSN:0161-1712
1687-0425

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