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arXiv · 1510.03632

Order Isomorphisms on Convex Functions in Windows

S. Artstein-Avidan·D. I. Florentin·V. D. Milman
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Abstract

In this paper we give a characterization of all order isomorphisms on some classes of convex functions. We deal with the class $Cvx(K)$ consisting of lower-semi-continuous convex functions defined on a convex set $K$, and its subclass $Cvx_0(K)$ of non negative functions attaining the value zero at the origin. We show that any order isomorphism on these classes must be induced by a point map on the epi-graphs of the functions, and determine the exact form of this map. To this end we study convexity preserving maps on subsets of ${\mathbb R}^n$, and also in this area we have some new interpretations, and proofs.

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BibTeXRIS

S. Artstein-Avidan, D. I. Florentin, V. D. Milman. 2015-10-13. Order Isomorphisms on Convex Functions in Windows. https://arxiv.org/abs/1510.03632

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