International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 49-55
doi:10.1155/S0161171285000047
Transformations which preserve convexity
Robert A. Fontenot1
and Frank Proschan2
1Department of Mathematics, Whitman College, Walla Walla 99362, Washington, USA
2Department of Statistics, Florida State University, Tallahassee 32306, Florida, USA
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.