TY - CHAP
T1 - Order isomorphisms on convex functions in windows
AU - Artstein-Avidan, Shiri
AU - Florentin, Dan
AU - Milman, Vitali
PY - 2012
Y1 - 2012
N2 - 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 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 , and also in this area we have some new interpretations, and proofs.
AB - 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 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 , and also in this area we have some new interpretations, and proofs.
UR - https://www.scopus.com/pages/publications/84865338389
U2 - 10.1007/978-3-642-29849-3_4
DO - 10.1007/978-3-642-29849-3_4
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AN - SCOPUS:84865338389
SN - 9783642298486
T3 - Lecture Notes in Mathematics
SP - 61
EP - 122
BT - Geometric Aspects of Functional Analysis
PB - Springer Verlag
ER -