Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 18 (2011), No. 3, 687--698Copyright Heldermann Verlag 2011 On the Infimum of a Quasiconvex Function over an Intersection. Application to the Distance Function Juan-Enrique Martínez Legaz Dep. d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, 08193 Bellaterra - Barcelona, Spain JuanEnrique.Martinez.Legaz@uab.es Antonio Martinón Dep. de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna - Tenerife, Spain anmarce@ull.es [Abstract-pdf] We give sufficient conditions for the infimum of a quasiconvex function $f$ over the intersection $\bigcap_{i\in I}R_{i}$ to agree with the supremum of the infima of $f$ over the $R_{i}$'s. We apply these results to the distance function in a normed space. Keywords: Quasiconvex functions, distance to the intersection. MSC: 54E35; 26-99 [ Fulltext-pdf  (142  KB)] for subscribers only.