Journal of Convex Analysis 17 (2010), No. 1, 095--101
Copyright Heldermann Verlag 2010
On the Continuous Representation of Quasiconcave Functions by Their Upper Level Sets
Philippe Bich
Paris School of Economics, Centre d'Economie de la Sorbonne, Université Paris I Panthéon, 106/112 Boulevard de l'Hôpital, 75013 Paris, France
philippe.bich@univ-paris1.fr
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.
Keywords: Quasiconcave, upper level set.
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