Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article
 


Journal of Convex Analysis 17 (2010), No. 1, 103--110
Copyright Heldermann Verlag 2010



Invertibility of Order-Reversing Transforms on Convex Functions

Stephen E. Wright
Dept. of Mathematics and Statistics, Miami University, Oxford, OH 45056, U.S.A.
wrightse@muohio.edu



The invertibility of an order-reversing transform on the class of proper lower semicontinuous convex functions is completely determined by the behavior of its composition with its putative inverse (and of the reverse composition) on the subclasses of continuous affine functions over the primal and dual spaces. This strengthens a recent result of Artstein-Avidan and Milman, which characterizes order-reversing transforms of convex functions as affine adjustments of the Legendre-Fenchel transform.

Keywords: Locally convex space, Legendre-Fenchel transform, convex duality.

MSC: 46N10, 52A41

[ Fulltext-pdf  (101  KB)] for subscribers only.