Geodesic
Invertibility of Order-Reversing Transforms on Convex Functions
Journal of convex analysis, Tome 17 (2010) no. 1, pp. 103-11 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 46N10, 52A41
Mots-clés : Locally convex space, Legendre-Fenchel transform, convex duality 
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     author = {S. E. Wright},
     title = {Invertibility of {Order-Reversing} {Transforms} on {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {103--11},
     year = {2010},
     volume = {17},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_1_JCA_2010_17_1_a8/}
}
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S. E. Wright. Invertibility of Order-Reversing Transforms on Convex Functions. Journal of convex analysis, Tome 17 (2010) no. 1, pp. 103-11. http://geodesic.mathdoc.fr/item/JCA_2010_17_1_JCA_2010_17_1_a8/