Paraconvex functions and paraconvex sets

Huynh Van Ngai¹ ; Jean-Paul Penot²

¹ Department of Mathematics Pedagogical University of Quynhon 170 An Duong Vuong Qui Nhon, Vietnam
² Laboratoire de Mathématiques Appliquées CNRS UMR 5142 Faculté des Sciences Av. de l'Université 64000 Pau, France

Studia Mathematica, Tome 184 (2008) no. 1, pp. 1-29

Résumé

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.

Détail

DOI : 10.4064/sm184-1-1

Keywords: study class functions which contains convex functions differentiable functions whose derivatives locally lipschitzian lderian class subclass class approximately convex functions enjoys refined properties introduce class sets whose associated distance functions type discuss properties metric projections sets under assumptions geometry banach spaces which embedded describe relations between sets functions