International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 49-55
doi:10.1155/S0161171285000047
Transformations which preserve convexity
1Department of Mathematics, Whitman College, Walla Walla 99362, Washington, USA
2Department of Statistics, Florida State University, Tallahassee 32306, Florida, USA
Received 7 January 1983
Copyright © 1985 Robert A. Fontenot and Frank Proschan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.