Paraconvex functions and paraconvex sets

Volume 184 / 2008

Huynh Van Ngai, Jean-Paul Penot Studia Mathematica 184 (2008), 1-29 MSC: 49J52, 46N10, 46T20. DOI: 10.4064/sm184-1-1


We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded. We describe some relations between such sets and functions.


  • Huynh Van NgaiDepartment of Mathematics
    Pedagogical University of Quynhon
    170 An Duong Vuong
    Qui Nhon, Vietnam
  • Jean-Paul PenotLaboratoire de Mathématiques Appliquées
    CNRS UMR 5142
    Faculté des Sciences
    Av. de l'Université
    64000 Pau, France

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