TY - JOUR

T1 - Order isomorphisms in windows

AU - Artstein-Avidan, Shiri

AU - Florentin, Dan

AU - Milman, Vitali

PY - 2011

Y1 - 2011

N2 - We characterize order preserving transforms on the class of lowersemi- continuous convex functions that are defined on a convex subset of Rn (a "window") and some of its variants. To this end, we investigate convexity preserving maps on subsets of ℝn. We prove that, in general, an order isomorphism is induced by a special convexity preserving point map on the epi-graph of the function. In the case of non-negative convex functions on K, where 0 Ie{cyrillic, ukrainian} K and f(0) = 0, one may naturally partition the set of order isomorphisms into two classes; we explain the main ideas behind these results.

AB - We characterize order preserving transforms on the class of lowersemi- continuous convex functions that are defined on a convex subset of Rn (a "window") and some of its variants. To this end, we investigate convexity preserving maps on subsets of ℝn. We prove that, in general, an order isomorphism is induced by a special convexity preserving point map on the epi-graph of the function. In the case of non-negative convex functions on K, where 0 Ie{cyrillic, ukrainian} K and f(0) = 0, one may naturally partition the set of order isomorphisms into two classes; we explain the main ideas behind these results.

KW - Convex functions

KW - Fractional linear maps

KW - Order isomorphisms

UR - http://www.scopus.com/inward/record.url?scp=84875910867&partnerID=8YFLogxK

U2 - 10.3934/era.2011.18.112

DO - 10.3934/era.2011.18.112

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AN - SCOPUS:84875910867

SN - 1935-9179

VL - 18

SP - 112

EP - 118

JO - Electronic Research Announcements in Mathematical Sciences

JF - Electronic Research Announcements in Mathematical Sciences

ER -