Paraconvex functions and paraconvex sets
Tom 184 / 2008
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.