Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Quasiconcave
  • upper level set

Suggested citation

P. Bich. “On the Continuous Representation of Quasiconcave Functions by Their Upper Level Sets.” Journal of Convex Analysis 17 (2010), No. 1, 95–101.

Copyright Heldermann Verlag 2010