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On Evenly Convex Sets and Functions

Margarita Rodríguez Álvarez
Departamento de Estadística e Investigación Operativa
Universidad de Alicante
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José Vicente Pérez
Departamento de Estadística
Universidad de Economía
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  • Abstract
    A subset of R^n is said to be evenly convex (e-convex, in breaf) if it is the intersection of some family (possibly empty) of open halfspaces. In this paper, we collect some published results which show that this large class of convex sets enjoys a lot of the well-known properties of the subclass of closed convex sets. We also consider functions whose epigraphs are e-convex sets, the so-called e-convex functions, and we show the main properties of this class of convex functions that contains the important class of lower semicontinuous convex functions.
  • Keywords: Closed convex sets, Evenly convex sets, Lower semicontinuous convex functions, Evenly convex functions.
  • AMS Subject classifications: 90C25, 90C34, 52A41.