The attainment set of the φ-envelope and genericity properties

• A. Cabot ^[1] ; A. Jourani ^[1] ; L. Thibault ^[2] ; D. Zagrodny ^[3]
  1. [1] University of Franche-Comté

     University of Franche-Comté

     Arrondissement de Besançon, Francia

     
  2. [2] University of Montpellier

     University of Montpellier

     Arrondissement of Montpellier, Francia

     
  3. [3] University of Łódź

     University of Łódź

     Łódź, Polonia

     

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• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 124, Nº 2, 2019, págs. 203-246
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The attainment set of the φ-envelope of a function at a given point is investigated. The inclusion of the attainment set of the φ-envelope of the closed convex hull of a function into the attainment set of the function is preserved in sufficiently general settings to encompass the case φ being a norm in a power not less than 1. The non-emptiness of the attainment set is guaranteed on generic subsets of a given space, in several fundamental cases.