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Journal of Convex Analysis 18 (2011), No. 3, 687--698
Copyright Heldermann Verlag 2011

On the Infimum of a Quasiconvex Function over an Intersection. Application to the Distance Function

Juan-Enrique MartŪnez Legaz
Dep. d'Economia i d'HistÚria EconÚmica, Universitat AutÚnoma de Barcelona, 08193 Bellaterra - Barcelona, Spain

Antonio Martinůn
Dep. de AnŠlisis MatemŠtico, Universidad de La Laguna, 38271 La Laguna - Tenerife, Spain


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

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