Geodesic
On the Continuous Representation of Quasiconcave Functions by Their Upper Level Sets
Journal of convex analysis, Tome 17 (2010) no. 1, pp. 95-101.

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We provide a continuous representation of quasiconcave functions by their upper level sets. A possible motivation is the extension to quasiconcave functions of a result by D. H. Hyers and S. M. Ulam [Proc. Amer. Math. Soc. 3(5) (1952) 821--828], which states that every approximately convex function can be approximated by a convex function.
Mots-clés : Quasiconcave, upper level set 
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P. Bich. On the Continuous Representation of Quasiconcave Functions by Their Upper Level Sets. Journal of convex analysis, Tome 17 (2010) no. 1, pp. 95-101. http://geodesic.mathdoc.fr/item/JCA_2010_17_1_JCA_2010_17_1_a7/