Paraconvex functions and paraconvex sets

• Autorzy: Huynh Van Ngai , Jean-Paul Penot
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46T20: Continuous and differentiable maps
• 49J52: Nonsmooth analysis
• 46N10: Applications in optimization, convex analysis, mathematical programming, economics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 184
• Numer: 1
• Strony: 1-29

Daty

wydano

2008

Twórcy

autor

Huynh Van Ngai

• Department of Mathematics, Pedagogical University of Quynhon, 170 An Duong Vuong, Qui Nhon, Vietnam

autor

Jean-Paul Penot

• Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Faculté des Sciences, Av. de l'Université, 64000 Pau, France

Identyfikatory

DOI

10.4064/sm184-1-1